Dr. Sameen Ahmed Khan
([email protected])
(Visiting Card,
Picture,
Pictures and the
BiographicalNote)
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 45+ Articles
from the Scopus
http://SameenAhmedKhan.webs.com/
http://www.imsc.res.in/~jagan/khancv.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 {p_{1} + j d}, j = 0 to k1

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206037.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206038.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206039.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206040.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206041.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206042.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206043.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206044.
(Friday the 03 February 2012).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A206045.
(Friday the 03 February 2012).

Sameen Ahmed Khan,
Table1: Integer Sequences for the difference for Primes in Arithmetic Progression with the minimal start
Sequence: {p_{1} + j d}, j = 0 to k1

Order k 
Minimal Start p_{1} 
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 p_{1} 
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 {p_{1} + j*(k#)}, j = 0 to k1
The minimal possible difference in an APk 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 AP2 with this difference: {2, 3}.
For k = 3, we have d = 2 and there is ONLY one AP3 with this difference: {3, 5, 7}.
For k = 4, we have d = 4# = 6 and AP4 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 AP5 with this difference: {5, 11, 17, 23, 29}.
For k = 6, we have d = 6# = 30 and AP6 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 AP7 with this difference:
{7, 157, 307, 457, 607, 757, 907}.

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A227281.
(Friday the 05 July 2013).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A227282.
(Friday the 05 July 2013).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A227283.
(Friday the 05 July 2013).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A227284.
(Friday the 05 July 2013).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A227285.
(Friday the 05 July 2013).

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 OnLine Encyclopedia of Integer Sequences,
published electronically at
http://oeis.org/A227286.
(Friday the 05 July 2013).

Sameen Ahmed Khan,
Table2: Integer Sequences for the first primes of APk 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*10^{9} 











13 
13# 
Sequence A227286 
14933623
 2085471361 
> 41*10^{9} 










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.
Research in ChargedParticle Beam Optics.
Research in Light Beam Optics.
Some Research Encounters:

Number Theory.

Crystallographic Studies of the 123Superconductors
(YBa_{2}Cu_{3}O_{7x} the Yttrium Barium Copper Oxide).

SOC: SelfOrganized Criticality (SandPiles).

Resistor Networks.

Quadratic Surfaces.

Salt Solutions.
60+
Technical
Writings
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215+
NonTechnical 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 acceleratorbased science. Its primary purpose is to
strengthen collaboration in acceleratorbased 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://icfausa.jlab.org/archive/newsletter.shtml
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Patents

Sameen Ahmed Khan,
Quadricmeter,
Official Journal of the Patent Office,
Issue No.
43/2008,
PartI,
pp.
25296
(24 October
2008).
Application No.:
2126/MUM/2008 A,
International Classification: B69G1/36,
Controller General of Patents Designs and Trade Marks, Government of India
(Logo).
http://ipindia.nic.in/ipr/patent/journal_archieve/journal_2008/patent_journal_2008.htm
http://ipindia.nic.in/ipr/patent/journal_archieve/journal_2008/pat_arch_102008/official_journal_24102008_part_i.pdf
http://www.patentoffice.nic.in/,
http://www.ipindia.nic.in/
(Logo) .
(patent in process, see the Quadricmeter).
(Click for a
MS Word Version,
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Quadricmeter).
Quadricmeter is the instrument devised to identify (distinguish) and measure the various
parameters (axis, foci, latera recta, directrix, etc.,) completely characterizing the important
class of surfaces known as the quadratic surfaces. Quadratic surfaces (also known as quadrics)
include a wide range of commonly encountered surfaces including, cone, cylinder, ellipsoid,
elliptic cone, elliptic cylinder, elliptic hyperboloid, elliptic paraboloid, hyperbolic cylinder,
hyperbolic paraboloid, paraboloid, sphere, and spheroid. Quadricmeter is a generalized form of
the conventional spherometer and the lesser known cylindrometer (also known as the "CylindroSpherometer"
and "SpheroCylindrometer").
With a conventional spherometer it was possible only to measure the radii of spherical surfaces.
Cylindrometer can measure the radii of curvature of a cylindrical surface in addition to the spherical
surface. In both the spherometer and the cylindrometer one assumes the surface to be either spherical
or cylindrical respectively. In the case of the quadricmeter, there are no such assumptions.
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the Curriculum Vitae
Fiftynine Page MS Word Version of the Curriculum Vitae
Three Page Resume in MS WORD
(view the
PS and the
PDF)
Eleven Page Resume in MS WORD
(view the
PS and the
PDF)
Fortyone 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]
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