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 Arithmetic Progression





Technical Writings




Integer Sequences for the difference for Primes in Arithmetic Progression with the minimal start Sequence {p1 + j d}, j = 0 to k-1

  1. Sameen Ahmed Khan,
    Sequence A206037: 2, 4, 8, 10, 14, 20, 28, 34, 38, 40, 50, 64, 68, 80, 94, 98, 104, 110, 124, 134, 154, 164, 178, 188, 190, 208, 220, 230, 238, 248, ...,
    Values of the difference d for 3 primes in arithmetic progression with the minimal start sequence {3 + j*d}, j = 0 to 2.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206037.
    (Friday the 03 February 2012).

  2. Sameen Ahmed Khan,
    Sequence A206038: 6, 12, 18, 42, 48, 54, 84, 96, 126, 132, 252, 348, 396, 426, 438, 474, 594, 636, 642, 648, 678, 804, 858, 1176, 1218, 1272, 1302, 1314, 1362, 1428, ...,
    Values of the difference d for 4 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 3.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206038.
    (Friday the 03 February 2012).

  3. Sameen Ahmed Khan,
    Sequence A206039: 6, 12, 42, 48, 96, 126, 252, 426, 474, 594, 636, 804, 1218, 1314, 1428, 1566, 1728, 1896, 2106, 2574, 2694, 2898, 3162, 3366, 4332, 4368, 4716, 4914, 4926, ...,
    Values of the difference d for 5 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 4.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206039.
    (Friday the 03 February 2012).

  4. Sameen Ahmed Khan,
    Sequence A206040: 30, 150, 930, 2760, 3450, 4980, 9150, 14190, 19380, 20040, 21240, 28080, 33930, 57660, 59070, 63600, 69120, 76710, 80340, 81450, 97380, 100920, 105960, ...,
    Values of the difference d for 6 primes in arithmetic progression with the minimal start sequence {7 + j*d}, j = 0 to 5.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206040.
    (Friday the 03 February 2012).

  5. Sameen Ahmed Khan,
    Sequence A206041: 150, 2760, 3450, 9150, 14190, 20040, 21240, 63600, 76710, 117420, 122340, 134250, 184470, 184620, 189690, 237060, 274830, 312000, 337530, 379410, ...,
    Values of the difference d for 7 primes in arithmetic progression with the minimal start sequence {7 + j*d}, j = 0 to 6.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206041.
    (Friday the 03 February 2012).

  6. Sameen Ahmed Khan,
    Sequence A206042: 1210230, 2523780, 4788210, 10527720, 12943770, 19815600, 22935780, 28348950, 28688100, 32671170, 43443330, 47330640, 51767520, 54130440, ...,
    Values of the difference d for 8 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 7.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206042.
    (Friday the 03 February 2012).

  7. Sameen Ahmed Khan,
    Sequence A206043: 32671170, 54130440, 59806740, 145727400, 224494620, 246632190, 280723800, 301125300, 356845020, 440379870, 486229380, 601904940, 676987920, ...,
    Values of the difference d for 9 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 8.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206043.
    (Friday the 03 February 2012).

  8. Sameen Ahmed Khan,
    Sequence A206044: 224494620, 246632190, 301125300, 1536160080, 1760583300, 4012387260, 4911773580, 7158806130, 8155368060, 15049362300, 15908029410, ...,
    Values of the difference d for 10 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 9.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206044.
    (Friday the 03 February 2012).

  9. Sameen Ahmed Khan,
    Sequence A206045: 1536160080, 4911773580, 25104552900, 77375139660, 83516678490, 100070721660, 150365447400, 300035001630, 318652145070, 369822103350, ...,
    Values of the difference d for 11 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 10.,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A206045.
    (Friday the 03 February 2012).

  10. Sameen Ahmed Khan,


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

Order
k

Minimal Start
p1

Common Factor for all the terms of the Sequence

n

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

2

2

1

Sequence A040976 1 3 5 9 11 15 17 21 27 29 35 39 41

3

3

2

Sequence A206037 2 4 8 10 14 20 28 34 38 40 50 64 68

4

5

3#

Sequence A206038 6 12 18 42 48 54 84 96 126 132 252 348 396

5

5

3#

Sequence A206039 6 12 42 48 96 126 252 426 474 594 636 804 1218

6

7

5#

Sequence A206040 30 150 930 2760 3450 4980 9150 14190 19380 20040 21240 28080 33930

7

7

5#

Sequence A206041 150 2760 3450 9150 14190 20040 21240 63600 76710 117420 122340 134250 184470

8

11

7#

Sequence A206042 1210230 2523780 4788210 10527720 12943770 19815600 22935780 28348950 28688100 32671170 43443330 47330640 51767520

9

11

7#

Sequence A206043 32671170 54130440 59806740 145727400 224494620 246632190 280723800 301125300 356845020 440379870 486229380 601904940 676987920

10

11

7#

Sequence A206044 224494620 246632190 301125300 1536160080 1760583300 4012387260 4911773580 7158806130 8155368060 15049362300 15908029410 18191167890 21238941150

11

11

7#

Sequence A206045 1536160080 4911773580 25104552900 77375139660 83516678490 100070721660 150365447400 300035001630 318652145070 369822103350 377344636200 511688932650 580028072610

12

13

11#

Sequence 1482708889200                        

13

13

11#

Sequence 9918821194590                        

14

17

13#

Sequence 266029822978920                        

15

17

13#

Sequence 266029822978920                        

16

17

13#

Sequence 11358256064006271420                        

17

17

13#

Sequence 341976204789992332560                        

18

19

17#

Sequence 128642760444772214170530                        

19

19

17#

Sequence 2166703103992332274919550                        

20

23 ???

19#

Sequence

???

                       

21

23 ???

19#

Sequence

???

                       

22

23 ???

19#

Sequence

???

                       

23

23 ???

19#

Sequence

???

                       

 

 

 

Sequence                          

Order
k

Minimal Start
p1

Common Factor for all the terms of the Sequence

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, 10# = 2.3.5.7 = 210.



Integer Sequences for the First primes of arithmetic progressions of k primes each with common difference k#
Minimal Difference Sequence {p1 + j*(k#)}, j = 0 to k-1


The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
The exceptional cases (for k < = 7) are k = 2, k = 3, k = 5 and k = 7.

For k = 2, we have d = 1 and there is ONLY one AP-2 with this difference: {2, 3}.

For k = 3, we have d = 2 and there is ONLY one AP-3 with this difference: {3, 5, 7}.

For k = 4, we have d = 4# = 6 and AP-4 is {5, 11, 17, 23} and is not unique.
The first primes is the Sequence A023271: 5, 11, 41, 61, 251, 601, 641, 1091, 1481, 1601, 1741, 1861, 2371, ...

For k = 5, we have d = 3# = 6 and there is ONLY one AP-5 with this difference: {5, 11, 17, 23, 29}.

For k = 6, we have d = 6# = 30 and AP-6 is {7, 37, 67, 97, 127, 157} and is not unique.
The first primes is the Sequence A156204: 7, 107, 359, 541, 2221, 6673, 7457, 10103, 25643, 26861, 27337, 35051, 56149, ...

For k = 7, we have d = 5*5# = 150 and there is ONLY one AP-7 with this difference: {7, 157, 307, 457, 607, 757, 907}.

  1. Sameen Ahmed Khan,
    Sequence A227281: 7, 11, 37, 107, 137, 151, 277, 359, 389, 401, 541, 557, 571, 877, 1033, 1493, 1663, 2221, 2251, 2879, 3271, 6269, 6673, 6703, 7457, 7487, 9431, 10103, 10133, 10567, 11981, 12457, 12973, 14723, 17047, 19387, 24061, 25643, 25673, 26861, 26891, 27337, 27367, ...,
    First primes of arithmetic progressions of 5 primes each with the common difference 30,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227281.
    (Friday the 05 July 2013).

  2. Sameen Ahmed Khan,
    Sequence A227282: 47, 179, 199, 409, 619, 829, 881, 1091, 1453, 3499, 3709, 3919, 10529, 10627, 10837, 10859, 11069, 11279, 14423, 20771, 22697, 30097, 30307, 31583, 31793, 32363, 41669, 75703, 93281, 95747, 120661, 120737, 120871, 120947, 129287, 140603, 153319, 153529, ...,
    First primes of arithmetic progressions of 7 primes each with the common difference 210,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227282.
    (Friday the 05 July 2013).

  3. Sameen Ahmed Khan,
    Sequence A227283: 199, 409, 619, 881, 3499, 3709, 10627, 10859, 11069, 30097, 31583, 120661, 120737, 153319, 182537, 471089, 487391, 564973, 565183, 825991, 1010747, 1280623, 1288607, 1288817, 1302281, 1302491, 1395209, 1982599, 2358841, 2359051, 2439571, 3161017, 3600521, ...,
    First primes of arithmetic progressions of 8 primes each with the common difference 210,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227283.
    (Friday the 05 July 2013).

  4. Sameen Ahmed Khan,
    Sequence A227284: 199, 409, 3499, 10859, 564973, 1288607, 1302281, 2358841, 3600521, 4047803, 17160749, 20751193, 23241473, 44687567, 50655739, 53235151, 87662609, 100174043, 103468003, 110094161, 180885839, 187874017, 192205147, 221712811, 243051733, 243051943, 304570103, ...,
    First primes of arithmetic progressions of 9 primes each with the common difference 210,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227284.
    (Friday the 05 July 2013).

  5. Sameen Ahmed Khan,
    Sequence A227285: 60858179, 186874511, 291297353, 1445838451, 2943023729, 4597225889, 7024895393, 8620560607, 8656181357, 19033631401, 20711172773, 25366690189, 27187846201, 32022299977, 34351919351, ...,
    First primes of arithmetic progressions of 11 primes each with the common difference 2310,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227285.
    (Friday the 05 July 2013).

  6. Sameen Ahmed Khan,
    Sequence A227286: 14933623, 2085471361, ...,
    First primes of arithmetic progressions of 13 primes each with the common difference 30030,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A227286.
    (Friday the 05 July 2013).

  7. Sameen Ahmed Khan,



Table-2: Integer Sequences for the first primes of AP-k with the difference k#

Order
k

Difference
k#

n

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

2

2#

Sequence A001359 3 5 11 17 29 41 59 71 101 107 137 149 179

3

3#

Sequence A023241 5 7 11 17 31 41 47 61 67 97 101 151 167

4

4#

Sequence A023271 5 11 41 61 251 601 641 1091 1481 1601 1741 1861 2371

5

5#

Sequence A227281 7 11 37 107 137 151 277 359 389 401 541 557 571

6

6#

Sequence A156204 7 107 359 541 2221 6673 7457 10103 25643 26861 27337 35051 56149

7

7#

Sequence A227282 47 179 199 409 619 829 881 1091 1453 3499 3709 3919 10529

8

8#

Sequence A227283 199 409 619 881 3499 3709 10627 10859 11069 30097 31583 120661 120737

9

9#

Sequence A227284 199 409 3499 10859 564973 1288607 1302281 2358841 3600521 4047803 17160749 20751193 23241473

10

10#

Sequence A094220 199 243051733 498161423 2490123989 5417375591 8785408259 8988840499 10385475431 11283287357 14384731703 18012540899 18346623637 21848966327

11

11#

Sequence A227285 60858179 186874511 291297353 1445838451 2943023729 4597225889 7024895393 8620560607 8656181357 19033631401 20711172773 25366690189 27187846201

12

12#

Sequence 147692845283 > 150*109                      

13

13#

Sequence A227286 14933623 2085471361 > 41*109                    

14

14#

Sequence 834172298383                        

15

15#

Sequence 894476585908771                        

16

16#

Sequence 1275290173428391                        

17

17#

Sequence 259268961766921                        

18

18#

Sequence 1027994118833642281                        

19

19#

Sequence 1424014323012131633                        

20

20#

Sequence 1424014323012131633                        

21

21#

Sequence 28112131522731197609                        

22

22# ???

Sequence

???

                       

23

23# ???

Sequence

???

                       

24

24# ???

Sequence

???

                       

 

 

Sequence                          

Order
k

Difference
k#

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, 10# = 2.3.5.7 = 210.


List of Integer Sequences for "Primes in 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

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MS WORD Version

200+ Non-Technical Writings (Popular Writings)

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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

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MS Word Version of the Patents




Integer Sequences

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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

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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]
Back to Mainpage of Sameen Ahmed Khan Curriculum Vitae Research in Charged-Particle Beam Optics Research in Light Beam Optics Technical Writings Books Patents (Quadricmeter) Integer Sequences Non-Technical Writings (Popular Writings) Multilingual Electronic Translation

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