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
Number Theory






Technical Writings




Integer Sequences for the difference for Primes in Arithmetic Progression with the minimal start Sequence {p + 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).


    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

    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). The following article gives the conditions under which, a GAP-k is a set of k primes in geometric-arithmetic progression.

  10. 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).

  11. 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).

  12. 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).

  13. 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).

  14. 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).

  15. 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).

  16. 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).

  17. 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).

  18. 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).

  19. 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).


    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}.

  20. 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).

  21. 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).

  22. 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).

  23. 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).

  24. 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).

  25. 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).

  26. Sameen Ahmed Khan,


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

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

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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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