Dr. Sameen Ahmed Khan             ([email protected])       (Visiting Card, Picture, Pictures and the Biographical-Note)
Assistant Professor,
Department of Mathematics and Sciences
College of Arts and Applied Sciences (CAAS)
Dhofar University (Logo)
Post Box No. 2509, Postal Code 211
Salalah
Dhofar
Sultanate of Oman (National Emblem).

List of 34+ Articles from the Scopus
http://SameenAhmedKhan.webs.com/
http://www.imsc.res.in/~jagan/khan-cv.html
http://sites.google.com/site/rohelakhan/
http://rohelakhan.webs.com/
http://www.du.edu.om/

Research Summary
Primes in Geometric-Arithmetic Progression



A geometric-arithmetic progression of primes is a set of k primes (denoted by GAP-k) of the form p1*r j + j*d for fixed p1, r and d and consecutive j, from j = 0 to k - 1. i.e, {p1, p1*r + d, p1*r 2 + 2 d, p1* r 3 + 3 d, ...}. For example 3, 17, 79 is a 3-term geometric-arithmetic progression (i.e, a GAP-3) with a = p1 = 3, r = 5 and d = 2. A GAP-k is said to be minimal if the minimal start p1 and the minimal ratio r are equal, i.e, p1 = r = p, where p is the smallest prime ≥ k. Such GAPs have the form p*p j + j*d. Minimal GAPs with different differences, d do exist. For example, the minimal GAP-5 (p1 = r = 5) has the possible differences, 84, 114, 138, 168, ... (see the Sequence A209204) and the minimal GAP-6 (p1 = r = 7) has the possible differences, 144, 1494, 1740, 2040, .... (see the Sequence A209205). A minimal GAP-k is further said to be absolutely minimal if the difference d is minimum. All the GAPs up to k = 12 in Table-1 are absolutely minimal. Table-2 has the integer sequences for the differences corresponding to the minimal GAPs up to k = 12. Table-3 has the miscellaneous examples for the non-minimal GAPs. The following article gives the conditions under which, a GAP-k is a set of k primes in geometric-arithmetic progression. Computational data was obtained using initially the Microsoft EXCEL (up to GAP-6 in Table-1) and then the versatile MATHEMATICA.


Technical Writings



Table-1: Absolutely Minimal GAPs: Primes in Geometric-Arithmetic Progression with minimal start p1, minimal ratio r and the minimal difference d.

Order
k

Minimal Start
p1

Minimal Ratio
r

Minimal Difference
d

Minimal Difference
d
Factorized (Theorem-2)

Primes of the form,
{p1*r n + n*d},
n = 0 to k - 1

Complete Set of k Primes

Digits of First

Digits of Last

2 2 2 1 1 2*2n + n {2, 5} 1 1
3 3 3 2 2 3*3n + 2n {3, 11, 31} 1 2
4 5 5 6 3*(2#) 5*5n + 3*(2#)n {5, 31, 137, 643} 1 3
5 5 5 84 14*(3#) 5*5n + 14*(3#)n {5, 109, 293, 877, 3461} 1 4
6 7 7 144 24*(3#) 7*7n + 24*(3#)n {7, 193, 631, 2833, 17383, 118369} 1 6
7 7 7 3324 554*(3#) 7*7n + 554*(3#)n {7, 3373, 6991, 12373, 30103, 134269, 843487} 1 6
8 11 11 62610 2087*(5#) 11*11n + 2087*(5#)n {11, 62731, 126551, 202471, 411491, 2084611, 19862831, 214797151} 2 9
9 11 11 903030 30101*(5#) 11*11n + 30101*(5#)n {11, 903151, 1807391, 2723731, 3773171, 6286711, 24905351, 220680091, 2365171931} 2 10
10 11 11 903030 30101*(5#) 11*11n + 30101*(5#)n {11, 903151, 1807391, 2723731, 3773171, 6286711, 24905351, 220680091, 2365171931, 25945551871} 2 11
11 11 11 443687580 14789586*(5#) 11*11n + 14789586*(5#)n {11, 443687701, 887376491, 1331077381, 1774911371, 2220209461, 2681612651, 3320171941, 5907448331, 29930612821, 289748546411} 2 12
12 13 13 81647160420 388796002*(7#) 13*13n + 388796002*(7#)n {13, 81647160589, 163294323037, 244941509821, 326589012973, 408240628909, 489945711037, 572345853661, 663781782733, 872682935629, 2608631998237, 24196203887101} 2 14
13 13 13   > 160*107*(7#)        
14-17 17 17   > 10*107*(5#)        
18 19 19   > 18*107*(7#)        
19 19 19   > 10*107*(11#)        
20-23 23 23   > 10*107*(11#)        
24-29 29 29   > 11*107*(13#)        
30-31 31 31   > 11*107*(13#)        
32-37 37 37   > 6*107*(19*11#)        
                 

Order
k

Minimal Start
p1

Minimal Ratio
r

Minimal Difference
d

Minimal Difference
d
Factorized (Theorem-2)

Primes of the form,
{p1*r n + n*d},
n = 0 to k - 1

Complete Set of k Primes

Digits of First

Digits of Last

n # is the Primorial, 2.3.5. ... p, p ≤ n. For example, 10# = 2.3.5.7 = 210.



Integer Sequences for the difference for Primes in Geometric-Arithmetic Progression with the minimal start, and minimal ratio Sequence {p*pj + j*d}, j = 0 to k-1

  1. Sameen Ahmed Khan,
    Sequence A209202: 2, 8, 10, 20, 22, 28, 38, 50, 52, 62, 70, 92, 98, 100, 118, 122, 128, 140, 142, 170, 202, 218, 220, 230, 232, 248, 260, 268, 272, 302, ...,
    Values of the difference d for the geometric-arithmetic progression {3*3j + j*d}, j = 0 to j = 2 to be a set of 3 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209202.
    (Tuesday the 06 March 2012).

  2. Sameen Ahmed Khan,
    Sequence A209203: 6, 12, 16, 28, 34, 36, 54, 76, 78, 84, 114, 124, 132, 138, 142, 148, 154, 166, 168, 208, 226, 258, 268, 288, 324, 348, 376, 414, 436, 442, ...,
    Values of the difference d for the geometric-arithmetic progression {5*5j + j*d}, j = 0 to j = 3 to be a set of 4 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209203.
    (Tuesday the 06 March 2012).

  3. Sameen Ahmed Khan,
    Sequence A209204: 84, 114, 138, 168, 258, 324, 348, 462, 552, 588, 684, 714, 744, 798, 882, 894, 972, 1176, 1602, 1734, 2196, 2256, 2442, 2478, 2568, 2646, ...,
    Values of the difference d for the geometric-arithmetic progression {5*5j + j*d}, j = 0 to j = 4 to be a set of 5 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209204.
    (Tuesday the 06 March 2012).

  4. Sameen Ahmed Khan,
    Sequence A209205: 144, 1494, 1740, 2040, 3324, 4044, 6420, 12804, 13260, 13464 13620, 15444, 25824, 31524, 31674, 31680, 32124, 33720, 38064, 40410, ...,
    Values of the difference d for the geometric-arithmetic progression {7*7j + j*d}, j = 0 to j = 5 to be a set of 6 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209205.
    (Tuesday the 06 March 2012).

  5. Sameen Ahmed Khan,
    Sequence A209206: 3324, 13260, 38064, 46260, 51810, 54510, 58914, 76050, 81510, 82434, 109800, 119340, 120714, 132390, 141480, 154254, 167904, 169734, 185040, ...,
    Values of the difference d for the geometric-arithmetic progression {7*7j + j*d }, j = 0 to j = 6 to be a set of 7 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209206.
    (Tuesday the 06 March 2012).

  6. Sameen Ahmed Khan,
    Sequence A209207: 62610, 165270, 420300, 505980, 669780, 903030, 932400, 1004250, 1052610, 1093080, 1230270, 1231020, 1248120, ...,
    Values of the difference d for the geometric-arithmetic progression {11*11j + j*d}, j = 0 to j = 7 to be a set of 8 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209207.
    (Tuesday the 06 March 2012).

  7. Sameen Ahmed Khan,
    Sequence A209208: 903030, 1004250, 3760290, 7296450, 7763520, 17988210, 28962390, 29956950, 33316320, 37265160, 39013800, 39768150, 43920480, 50110620, 54651480, 56388810, 74306610, 74679810, 75911850, 89115210, 92619690, 98518800, ...,
    Values of the difference d for the geometric-arithmetic progression {11*11j + j*d }, j = 0 to j = 8 to be a set of 9 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209208.
    (Tuesday the 06 March 2012).

  8. Sameen Ahmed Khan,
    Sequence A209209: 903030, 17988210, 28962390, 39768150, 74306610, 89115210, 116535300, 173227980, 186013380, 237952050, 359613030, 386317920, 392253990, 443687580, 499153200, 548024610, 591655080, ...,
    Values of the difference d for the geometric-arithmetic progression {11*11j + j*d }, j = 0 to j = 9 to be a set of 10 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209209.
    (Tuesday the 06 March2012).

  9. Sameen Ahmed Khan,
    Sequence A209210: 443687580, 591655080, 1313813550, 2868131100, 3525848580, 3598823970, 4453413120, 6075076800, 6644124480, 7429693770, 9399746580, 11801410530, ...,
    Values of the difference d for the geometric-arithmetic progression {11*11j + j*d }, j = 0 to j = 10 to be a set of 11 primes,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at http://oeis.org/A209210.
    (Tuesday the 06 March 2012).

  10. Sameen Ahmed Khan,
    Sequence A227280: 81647160420, 170655787050, 211212209880, 227961624450, ...,
    Values of the difference d for 12 primes in geometric-arithmetic progression with the minimal sequence {13*13j + j*d}, j = 0 to 11,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227280.
    (Friday the 05 July 2013).

  11. Sameen Ahmed Khan,


Table-2: Integer Sequences for the difference for Primes in Geometric-Arithmetic Progression with the minimal start and minimal ratio Sequence: {p1*pj + j*d}, j = 0 to k-1

Order
k

Minimal Start
p1

Minimal Ratio
r

Common Factor for all the terms of the Sequence
(Theorem-2)

n

Sequence A000027
1 2 3 4 5 6 7 8 9 10 11 12 13

2

2

2

1

Sequence A172367 1 3 7 9 13 15 19 25 27 33 37 39 43

3

3

3

2

Sequence A209202 2 8 10 20 22 28 38 50 52 62 70 92 98

4

5

5

2

Sequence A209203 6 12 16 28 34 36 54 76 78 84 114 124 132

5

5

5

3#

Sequence A209204 84 114 138 168 258 324 348 462 552 588 684 714 744

6

7

7

3#

Sequence A209205 144 1494 1740 2040 3324 4044 6420 12804 13260 13464 13620 15444 25824

7

7

7

3#

Sequence A209206 3324 13260 38064 46260 51810 54510 58914 76050 81510 82434 109800 119340 120714

8

11

11

5#

Sequence A209207 62610 165270 420300 505980 669780 903030 932400 1004250 1052610 1093080 1230270 1231020 1248120

9

11

11

5#

Sequence A209208 903030 1004250 3760290 7296450 7763520 17988210 28962390 29956950 33316320 37265160 39013800 39768150 43920480

10

11

11

5#

Sequence A209209 903030 17988210 28962390 39768150 74306610 89115210 116535300 173227980 186013380 237952050 359613030 386317920 392253990

11

11

11

5#

Sequence A209210 443687580 591655080 1313813550 2868131100 3525848580 3598823970 4453413120 6075076800 6644124480 7429693770 9399746580 11801410530 12450590250

12

13

13

7#

Sequence A227280 81647160420 170655787050 211212209880 227961624450 > 160*107*(7#)                

13

13 ???

13 ???

7#

Sequence > 160*107*(7#)                        

14

17 ???

17 ???

5#

Sequence > 10*107*(5#)                        

15

17 ???

17 ???

5#

Sequence > 10*107*(5#)                        

16

17 ???

17 ???

5#

Sequence > 10*107*(5#)                        

17

17 ???

17 ???

5#

Sequence > 10*107*(5#)                        

18

19 ???

19 ???

7#

Sequence > 18*107*(7#)                        

19

19 ???

19 ???

11#

Sequence > 10*107*(11#)                        

 

 

 

 

Sequence                          

Order
k

Minimal Start
p1

Minimal Ratio
r

Common Factor for all the terms of the Sequence
(Theorem-2)

n

Sequence A000027
1 2 3 4 5 6 7 8 9 10 11 12 13

n # is the Primorial, 2.3.5. ... p, p ≤ n. For example, 12# = 2.3.5.7.11 = 2310.



Table-3: Miscellaneous examples of Primes in Geometric-Arithmetic Progression

Order
k

Starting Prime
p1

  Ratio  
r

 Difference 
d

  Difference  
d
   Factorized    
(Theorem-2)

Primes of the form,
{p1*r n + n*d},
n = 0 to k - 1

Complete Set of k Primes
GAP-k

Digits of First

Digits of Last

2 2 5 7 7 2*5n + 7n {2, 7} 1 2
2 13 80 53 53 13*80n + 53n {13, 1093} 1 4
2 M4253 = 24253 - 1 3 1358 679*(2) (24253 - 1)*3n + 679*(2)n Titanic GAP-2 1281 1281
2 M4423 = 24423 - 1 7 802 401*(2) (24423 - 1)*7n + 401*(2)n Titanic GAP-2 1332 1333
                 
3 5 7 24 4*(3#) 5*7n + 4*(3#)n {5, 59, 293} 1 3
3 M127 = 2127 - 1 3 7390 3695*(2) (2127 - 1)*3n + 3695*(2)n   39 40
3 M521 = 2521 - 1 3 1106 553*(2) (2521 - 1)*3n + 553*(2)n   157 158
3 M521 = 2521 - 1 19 26190*(2127 - 1) 4365*(3#)*(2127 - 1) (2521 - 1)*19n + 4365*(3#)*(2127 - 1)n   157 160
3 M4253 = 24253 - 1 19 2085660 347610*(3#) (24253 - 1)*19n + 347610*(3#)n Titanic GAP-3 1281 1283
3 M4423 = 24423 - 1 7 2330142 388357*(3#) (24423 - 1)*7n + 388357*(3#)n Titanic GAP-3 1332 1334
                 
4 11 35 24 12*(2#) 11*35n + 12*(2#)n {11, 409, 13523, 471697} 2 6
4 M521 = 2521 - 1 5 67872 33936*(2#) (2521 - 1)*5n + 33936*(2#)n   157 159
                 
5 47 M31 = 231 - 1 = 2147483647 81324 13554*(3#) 47*(231 - 1)n + 13554*(3#)n   2 39
5 M31 = 231 - 1 31 52440 1748*(5#) (231 - 1)*31n + 1748*(5#)n {2147483647, 66572045497, 2063731889647, 63975685485097, 1983246245370847} 10 16
                 
6 19 13 66 11*(3#) 19*13n + 11*(3#)n {19, 313, 3343, 41941, 542923, 7054897} 2 7
6 M31 = 231 - 1 31 135810 4527*(5#) (231 - 1)*31n + 4527*(5#)n {2147483647, 66572128867, 2063732056387, 63975685735207, 1983246245704327, 61480633600672747} 10 17
                 
7 17 13 588 98*(3#) 17*13n + 98*(3#)n {17, 809, 4049, 39113, 487889, 6314921, 82059281} 2 8
7 99538463 11 293550 9785*(5#) 17*13n + 9785*(5#)n {99538463, 1095216643, 12044741123, 132486574903, 1457343810983, 16030770472363, 176338460812043} 8 15
7 M31 = 231 - 1 31 51974610 1732487*(5#) (231 - 1)*31n + 1732487*(5#)n {2147483647, 66623967667, 2063835733987, 63975841251607, 1983246453059527, 61480633859866747, 1905899641911652267} 10 19
                 
8 11 13 427140 71190*(3#) 11*13n + 71190*(3#)n {11, 427283, 856139, 1305587, 2022731, 6219923, 55657739, 693223667} 2 9
8 13 11 3720 124*(5#) 13*11n + 124*(5#)n {13, 3863, 9013, 28463, 205213, 2112263, 23052613, 253359263} 2 9
8 31 13 3840 640*(3#) 31*13n + 640*(3#)n {31, 4243, 12919, 79627, 900751, 11529283, 149654119, 1945230907} 2 10
8 M31 = 231 - 1 31 381925530 12730851*(5#) (231 - 1)*31n + 12730851*(5#)n {2147483647, 66953918587, 2064495635827, 63976831104367, 1983247772863207, 61480635509621347, 1905899643891357787, 59082888892267421527} 10 20
                 
9 11 13 2520 84*(5#) 11*13n + 84*(5#)n {11, 2663, 6899, 31727, 324251, 4096823, 53110019, 690251327, 8973058091} 2 10
9 M31 = 231 - 1 31 420680430 = 14022681 14022681*(5#) (231 - 1)*31n + 14022681*(5#)n {2147483647, 66992673487, 2064573145627, 63976947369067, 1983247927882807, 61480635703395847, 1905899644123887187, 59082888892538705827, 1831569555580777670767} 10 22
                 
10 13 11 343770 11459*(5#) 13*11n + 11459*(5#)n {13, 343913, 689113, 1048613, 1565413, 3812513, 25092913, 255739613, 2789415613, 30656413913} 2 11
10 17 17 231000 7700(5#) 17*17n + 7700*(5#)n {17, 231289, 466913, 776521, 2343857, 25292569, 411724673, 6977374441, 118589724497, 2015995979449} 2 13
10 M31 = 231 - 1 31 1369341570 45644719*(5#) (231 - 1)*31n + 45644719*(5#)n {2147483647, 67941334627, 2066470467907, 63979793352487, 1983251722527367, 61480640446701547, 1905899649815854027, 59082888899179333807, 1831569555588366959887, 56778656222912103121267} 10 23
                 
11 13 11 3877860 129262*(5#) 13*11n + 129262*(5#)n {13, 3878003, 7757293, 11650883, 15701773, 21482963, 46297453, 280478243, 2817688333, 30688220723, 337225298413} 2 12
11 13 13 206479140 983234*(7#) 13*13n + 983234*(7#)n {13, 206479309, 412960477, 619465981, 826287853, 1037222509, 1301623357, 2261084701, 12256332493, 139716804109, 1794225185437} 2 13
11 17 17 311233230 10374441*(5#) 17*17n + 10374441*(5#)n {17, 311233519, 622471373, 933783211, 1246352777, 1580303719, 2277738053, 9154390051, 121077742337, 2018794999519, 34275008639933} 2 14
11 23 23 7601809710 253393657*(5#) 23*23n + 253393657*(5#)n {23, 7601810239, 15203631587, 22805708971, 30413675183, 38157084439, 49015683707, 131523653251, 1861967139143, 41494927501039, 952885776011027} 2 15
11 79 79 26045591952099720 868186398403324*(5#) 79*79n + 868186398403324*(5#)n {79, 26045591952105961, 52091183904692479, 78136775895249241, 104182370885455279, 130228202847954121, 156292755621584479, 183836252474604601, 328216331599416079, 9702686410195744681, 748254266447041926079} 2 21
11 101 19 118617870 3953929*(5#) 101*19n + 3953929*(5#)n {101, 118619789, 237272201, 356546369, 487633901, 843175349, 5463341201, 91111370729, 1716288810101, 32592525036509, 619238878216601} 3 15
11 103 103 6471123701482440 215704123382748*(5#) 103*103n + 215704123382748*(5#)n {103, 6471123701493049, 12942247404057607, 19413371216998201, 25884506398670503, 32356812559708729, 38949729595437127, 57965566724253241, 1356542173441104103, 134449878047725534009, 13842403418481470605447} 3 23
11 M19 = 219 - 1 = 524287 19 2130664290 71022143*(5#) (219 - 1)*19n + 71022143*(5#)n {524287, 2140625743, 4450596187, 9988077403, 76848263287, 1308839837863, 24678327797587, 468660247075123, 8904278361391087, 169180984181437183, 3214438356410355787} 6 19
                 
12 19 19 21586975410 719565847*(5#) 19*19n + 719565847*(5#)n {19, 21586975771, 43173957679, 64761056551, 86350377739, 107981922931, 130415724199, 168092390911, 495383501059, 6325349036491, 116706128652319, 2213552375795671} 2 16
12 29 29 580640320260 2764953906*(7#) 29*29n + 2764953906*(7#)n {29, 580640321101, 1161280664909, 1741921668061, 2322581792189, 2903796424621, 3501091797869, 4564728654781, 19152268537949, 425932996182541, 12206316168908429, 353821170248991901} 2 18
12 31 31 2107142397360 70238079912*(5#) 31*31n + 70238079912*(5#)n {31, 2107142398321, 4214284824511, 6321428115601, 8428598218591, 10536599490481, 12670366998271, 15602887818961, 43296761339551, 838592568557041, 25429548320378431, 787685962354920721} 2 18
                 
13 19 19 21586975410 719565847*(5#) 19*19n + 719565847*(5#)n {19, 21586975771, 43173957679, 64761056551, 86350377739, 107981922931, 130415724199, 168092390911, 495383501059, 6325349036491, 116706128652319, 2213552375795671, 42053242505961979} 2 17
                 
14                
                 
15                
                 
16                
                 
17                
                 

Order
k

Starting Prime
p1

Ratio
r

Difference
d

Difference
d
Factorized (Theorem-2)

Primes of the form,  
{p1*r n + n*d},
n = 0 to k - 1

Complete Set of k Primes
GAP-k

Digits of First

Digits of Last

n # is the Primorial, 2.3.5. ... p, p ≤ n. For example, 9# = 2.3.5.7 = 210.

M19 = 219 - 1,   M31 = 231 - 1,   M127 = 2127 - 1,   M521 = 2521 - 1,   M4253 = 24253 - 1,   and M4423 = 24423 - 1 are Mersenne Primes.

Titanic Primes have 1,000 or more decimal digits.   Gigantic Primes have 10,000 or more decimal digits.



List of Integer Sequences for "Primes in Geometric-Arithmetic Progression" from the http://oeis.org/ (Logo).

http://oeis.org/wiki/User:Sameen_Ahmed_Khan at OEIS Wiki (Logo).


List of 35+ Writeups from the INSPIRE HEP (Logo), Originally SLAC SPIRES (Logo). List of 20+ Writeups from the LANL E-Print archive (see the Atom Feeds).


Some Publications from the American Mathematical Society (AMS, Logo) MathSciNet (Logo). List of 250+ Writeups from the Google Scholar (Logo).

Research in Charged-Particle Beam Optics.

Research in Light Beam Optics.

Some Research Encounters:

  1. Number Theory.

  2. Crystallographic Studies of the 123-Superconductors (YBa2Cu3O7-x the Yttrium Barium Copper Oxide).

  3. SOC: Self-Organized Criticality (SandPiles).

  4. Resistor Networks.

  5. Quadratic Surfaces.

  6. Salt Solutions.


60+ Technical Writings

Click here for a LaTeX/MiKTeX Derived DVI Version, PS Version or/and PDF Version of the Technical Writings

MS WORD Version

200+ Non-Technical Writings (Popular Writings)

Click here for a LaTeX/MiKTeX Derived DVI Version, PS Version or/and PDF Version of the Non-Technical Writings (Popular Writings)
MS WORD Version


In March 2005, I was appointed as the Regular Correspondent for the International Committee for Future Accelerators (ICFA, Logo) Beam Dynamics Panel Newsletters (Logo), for the region of Middle East & Africa. ICFA, the International Committee for Future Accelerators (Logo), provides a forum to discuss and implement plans for further promoting collaborative accelerator-based science. Its primary purpose is to strengthen collaboration in accelerator-based science, to encourage future projects, and to make recommendations to governments. See the International Committee for Future Accelerators (ICFA, Logo) Beam Dynamics Panel Newsletter (Logo), No. 36 (April 2005).
http://icfa-usa.jlab.org/archive/newsletter.shtml

Patents

Click for a LaTeX/MiKTeX Derived DVI Version, PS Version or/and PDF Version of the Patents

MS Word Version of the Patents




Integer Sequences

Click for a LaTeX/MiKTeX Derived DVI Version, PS Version or/and PDF Version of the Integer Sequences

MS WORD Version of the Integer Sequences

MS EXCEL Version of the Integer Sequences

List of the 35 Integer Sequences from the http://oeis.org/ (Logo)

http://oeis.org/wiki/User:Sameen_Ahmed_Khan.


Curriculum Vitae

Click here for a LaTeX/MiKTeX Derived DVI Version, PS Version or/and PDF Version of the Curriculum Vitae

Fifty-six Page MS Word Version of the Curriculum Vitae

Three Page Resume in MS WORD (view the PS and the PDF)

Ten Page Resume in MS WORD (view the PS and the PDF)

Thirty-eight Page CV in MS WORD (view the PS and the PDF)

Versión en Español Octubre 2001 DVI Version, PS Version, O/Y PDF Version


MECIT Report (for the stay at the Middle East College of Information Technology, Logo)

SCOT Report (for the stay at the Salalah College of Technology, Logo)

The Oman Report: The Consolidated Report of my stay in the Sultanate of Oman (National Emblem); at the Middle East College of Information Technology (MECIT, Logo), Muscat and the Salalah College of Technology (SCOT, Logo), Salalah.
My Erdös Number and Einstein Number
My Academic Genealogy
Mathematics Genealogy Project (Logo, Entry No. 93310)

VIDWAN: EXPERT DATABASE
Online Profiles of Academic Community of Indian Universities
(Logo)
Persistent URL: https://vidwan.inflibnet.ac.in/profile/41991
View the Photographs, http://www.flickr.com/photos/rohelakhan/ at http://www.flickr.com/

For Copies of Preprints and Additional Information: [email protected]
Patents (Quadricmeter)
Back to Mainpage of Sameen Ahmed Khan Curriculum Vitae Research in Charged-Particle Beam Optics Research in Light Beam Optics Technical Writings Books Integer Sequences Non-Technical Writings (Popular Writings) Multilingual Electronic Translation

Thanks for your visit. You are visitor no.
http://www.imsc.res.in/~jagan/khan-cv.html       http://SameenAhmedKhan.webs.com/       http://sites.google.com/site/rohelakhan/       http://rohelakhan.webs.com/      

This page was born in March 1996 at the
The Institute of Mathematical Sciences (MATSCIENCE/IMSc, Logo), Chennai (Madras) INDIA (National Emblem).
© Last updated on Friday, the 01 July 2016