Sameen Ahmed Khan - cp's OEIS frontend

A227280 Values of the difference d for 12 primes in geometric-arithmetic progression with the minimal sequence {1313^j + jd}, j = 0 to 11.

81647160420, 170655787050, 211212209880, 227961624450

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

Primality requires d to be multiple of 7# = 2*3*5*7 = 210.

Fifth term is > (1600*10^6)*(210) = 336000000000.

			d = 170655787050 then {13*13^j + j*d}, j = 0 to 11, is {13, 170655787219, 341311576297, 511967389711, 682623519493, 853283762059, 1023997470817, 1195406240071, 1375850795773, 1673760575299, 3498718264537, 25175298780031}, which is 12 primes in geometric-arithmetic progression.

Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).

Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209208, A209209, A209210.

Clear[p]; p = 13; gapset12d = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d, p*p^3 + 3*d, p*p^4 + 4*d, p*p^5 + 5*d, p*p^6 + 6*d, p*p^7 + 7*d, p*p^8 + 8*d, p*p^9 + 9*d, p*p^10 + 10*d, p*p^11 + 11*d}] == {True, True, True, True, True, True, True, True, True, True, True, True}, AppendTo[gapset12d, d]], {d, 2, 10^11, 2}]; gapset12d

A227286 First primes of arithmetic progressions of 13 primes each with the common difference 30030.

Original entry on oeis.org

14933623, 2085471361, 132420258931, 185041386139, 682539280751, 834172298383, 834172328413, 856378247603, 856378277633, 888867525577, 931115864233, 1059709587163, 1345030977911, 1360910561113, 1578280523803, 1973348047529, 1988253536611, 2083502941613

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

The minimal possible difference in an arithmetic progression of k primes is conjectured to be k# = A034386(k) for all k > 7. 13# = 30030.

			p = 2085471361 then the AP-13 is {2085471361, 2085501391, 2085531421, 2085561451, 2085591481, 2085621511, 2085651541, 2085681571, 2085711601, 2085741631, 2085771661, 2085801691, 2085831721} with the difference 13# = 2*3*5*7*11*13 = 30030.

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227285.

Clear[p]; d = 30030; ap13p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d, p + 9*d, p + 10*d, p + 11*d, p + 12*d}] == {True, True, True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap13p, p]], {p, 3, 41*10^9, 2}]; ap13p

More terms from Jens Kruse Andersen, Jun 27 2014

A227285 First primes of arithmetic progressions of 11 primes each with the common difference 2310.

Original entry on oeis.org

60858179, 186874511, 291297353, 1445838451, 2943023729, 4597225889, 7024895393, 8620560607, 8656181357, 19033631401, 20711172773, 25366690189, 27187846201, 32022299977, 34351919351

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

16th term is greater than 40*10^9.

			p = 186874511 then the AP-11 is {186874511, 186876821, 186879131, 186881441, 186883751, 186886061, 186888371, 186890681, 186892991, 186895301, 186897611} with the difference 11# = 2*3*5*7*11 = 2310.

Zak Seidov, Table of n, a(n) for n = 1..21

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227286.

Clear[p]; d = 2310; ap11p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d, p + 9*d, p + 10*d}] == {True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap11p, p]], {p, 3, 40*10^9, 2}]; ap11p
ap11Q[n_]:=AllTrue[Rest[NestList[2310+#&,n,10]],PrimeQ]; Select[Prime[ Range[ 148*10^7]],ap11Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* The program will take a long time to run *) (* Harvey P. Dale, Oct 27 2019 *)

a(16)-a(21) from Zak Seidov, Jul 07 2014

A227284 First primes of arithmetic progressions of 9 primes each with the common difference 210.

Original entry on oeis.org

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

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

When a(n+1) = a(n) + 210, as for n = 1, 25, ..., then a(n) is in A094220: start of AP of 10 primes with common distance 210. - M. F. Hasler, Jan 02 2020

			p = 409 then the AP-9 is {409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089} with the difference 9# = 2*3*5*7 = 210.

Sameen Ahmed Khan, Table of n, a(n) for n = 1..47
OEIS wiki, Primes in arithmetic progression.

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227285, A227286.

Clear[p]; d = 210; ap9p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d}] == {True, True, True, True, True, True, True, True, True}, AppendTo[ap9p, p]], {p, 3, 10^9, 2}]; ap9p

v=[1..8]*210; forprime(p=1,,for(i=1,#v,isprime(p+v[i])||next(2));print1(p",")) \\ M. F. Hasler, Jan 02 2020

A227283 First primes of arithmetic progressions of 8 primes each with the common difference 210.

Original entry on oeis.org

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

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

Sameen Ahmed Khan, Table of n, a(n) for n = 1..150

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227284, A227285, A227286.

Clear[p]; d = 210; ap8p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d}] == {True, True, True, True, True, True, True, True}, AppendTo[ap8p, p]], {p, 3, 3000000, 2}]; ap8p
Select[Prime[Range[260000]],AllTrue[NestList[#+210&,#,7],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 03 2018 *)

A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210.

Original entry on oeis.org

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

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

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}.

			p = 179 then the AP-5 is {179, 389, 599, 809, 1019, 1229, 1439} with the difference 7# = 210.

Sameen Ahmed Khan and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2484 terms from Khan)

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227283, A227284, A227285, A227286.

Clear[p]; d = 210; ap7p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d}] == {True, True, True, True, True, True, True}, AppendTo[ap7p, p]], {p, 3, 10^9, 2}]; ap7p
Select[Prime[Range[15000]],And@@PrimeQ[NestList[210+#&,#,6]]&] (* Harvey P. Dale, Nov 16 2013 *)

is(p)=forstep(k=p,p+1260,210,if(!isprime(k),return(0)));1 \\ Charles R Greathouse IV, Dec 19 2013

A227281 First primes of arithmetic progressions of 5 primes each with the common difference 30.

Original entry on oeis.org

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

Offset: 1

Sameen Ahmed Khan, Jul 05 2013

nonn

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

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

			p = 11 then {11, 11 + 1*30, 11 + 2*30, 11 + 3*30, 11 + 4*30} = {11, 41, 71, 101, 131}, which is 5 primes in arithmetic progression with the difference 5# = 30.

Sameen Ahmed Khan, Table of n, a(n) for n = 1..1184

Cf. A001359, A023241, A023271, A094220, A156204, A227282, A227283, A227284, A227285, A227286.

Clear[p]; d = 30; ap5p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d}] == {True, True, True, True, True}, AppendTo[ap5p, p]], {p, 3, 25000, 2}]; ap5p

A209210 Values of the difference d for 11 primes in geometric-arithmetic progression with the minimal sequence {1111^j + jd}, j = 0 to 10.

Original entry on oeis.org

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

Offset: 1

Sameen Ahmed Khan, Mar 06 2012

nonn

A geometric-arithmetic progression of primes is a set of k primes (denoted by GAP-k) of the form p r^j + j d for fixed p, r and d and consecutive j. Symbolically, for r = 1, this sequence simplifies to the familiar primes in arithmetic progression (denoted by AP-k). The computations were done without any assumptions on the form of d. Primality requires d to be multiple of 5# = 30 and coprime to 11.

			d = 591655080 then {11*11^j + j*d}, j = 0 to 10, is {11, 591655201, 1183311491, 1774979881, 2366781371, 2960046961, 3569417651, 4355944441, 7091188331, 31262320321, 291228221411}, which is 11 primes in geometric-arithmetic progression.

Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).

Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209208, A209209.

p = 11; gapset11d = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d, p*p^3 + 3*d, p*p^4 + 4*d, p*p^5 + 5*d, p*p^6 + 6*d, p*p^7 + 7*d, p*p^8 + 8*d, p*p^9 + 9*d, p*p^10 + 10*d}] == {True, True, True, True, True, True, True, True, True, True, True}, AppendTo[gapset11d, d]], {d, 0, 10^8, 2}]

A209209 Values of the difference d for 10 primes in geometric-arithmetic progression with the minimal sequence {1111^j + jd}, j = 0 to 9.

Original entry on oeis.org

903030, 17988210, 28962390, 39768150, 74306610, 89115210, 116535300, 173227980, 186013380, 237952050, 359613030, 386317920, 392253990, 443687580, 499153200, 548024610, 591655080, 652133160, 665780640, 705583830, 758828310, 910046550, 920546160, 921847290

Offset: 1

Sameen Ahmed Khan, Mar 06 2012

nonn

A geometric-arithmetic progression of primes is a set of k primes (denoted by GAP-k) of the form p r^j + j d for fixed p, r and d and consecutive j. Symbolically, for r = 1, this sequence simplifies to the familiar primes in arithmetic progression (denoted by AP-k). The computations were done without any assumptions on the form of d. Primality requires d to be multiple of 5# = 30 and coprime to 11.

			d = 17988210 then {11*11^j + j*d}, j = 0 to 9, is {11, 17988331, 35977751, 53979271, 72113891, 91712611, 127416431, 340276351, 2501853371, 26099318491}, which is 10 primes in geometric-arithmetic progression.

Sameen Ahmed Khan, Table of n, a(n) for n = 1..96
Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).

Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209208, A209210.

p = 11; gapset10d = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d, p*p^3 + 3*d, p*p^4 + 4*d, p*p^5 + 5*d, p*p^6 + 6*d, p*p^7 + 7*d, p*p^8 + 8*d, p*p^9 + 9*d}] == {True, True, True, True, True, True, True, True, True, True}, AppendTo[gapset10d, d]], {d, 0, 10^8, 2}]

A209208 Values of the difference d for 9 primes in geometric-arithmetic progression with the minimal sequence {1111^j + jd}, j = 0 to 8.

Original entry on oeis.org

903030, 1004250, 3760290, 7296450, 7763520, 17988210, 28962390, 29956950, 33316320, 37265160, 39013800, 39768150, 43920480, 50110620, 54651480, 56388810, 74306610, 74679810, 75911850, 89115210, 92619690, 98518800, 108718080, 116535300, 116958450, 117671820

Offset: 1

Sameen Ahmed Khan, Mar 06 2012

nonn

A geometric-arithmetic progression of primes is a set of k primes (denoted by GAP-k) of the form p r^j + j d for fixed p, r and d and consecutive j. Symbolically, for r = 1, this sequence simplifies to the familiar primes in arithmetic progression (denoted by AP-k). The computations were done without any assumptions on the form of d. Primality requires d to be multiple of 5# = 30 and coprime to 11.

			d = 1004250 then {11*11^j + j*d}, j = 0 to 8, is {11, 1004371, 2009831, 3027391, 4178051, 6792811, 25512671, 221388631, 2365981691}, which is 9 primes in geometric-arithmetic progression.

Sameen Ahmed Khan, Table of n, a(n) for n = 1..539
Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).

Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209209, A209210.

p = 11; gapset9d = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d, p*p^3 + 3*d, p*p^4 + 4*d, p*p^5 + 5*d, p*p^6 + 6*d, p*p^7 + 7*d, p*p^8 + 8*d}] == {True, True, True, True, True, True, True, True, True}, AppendTo[gapset9d, d]], {d, 0, 10^8, 2}]

cp's OEIS Frontend

User: Sameen Ahmed Khan

A227280 Values of the difference d for 12 primes in geometric-arithmetic progression with the minimal sequence {13*13^j + j*d}, j = 0 to 11.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A227286 First primes of arithmetic progressions of 13 primes each with the common difference 30030.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A227285 First primes of arithmetic progressions of 11 primes each with the common difference 2310.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A227284 First primes of arithmetic progressions of 9 primes each with the common difference 210.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A227283 First primes of arithmetic progressions of 8 primes each with the common difference 210.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A227281 First primes of arithmetic progressions of 5 primes each with the common difference 30.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A209210 Values of the difference d for 11 primes in geometric-arithmetic progression with the minimal sequence {11*11^j + j*d}, j = 0 to 10.

Views

Author

Keywords

Comments

Examples

A227280 Values of the difference d for 12 primes in geometric-arithmetic progression with the minimal sequence {1313^j + jd}, j = 0 to 11.

A209210 Values of the difference d for 11 primes in geometric-arithmetic progression with the minimal sequence {1111^j + jd}, j = 0 to 10.

A209209 Values of the difference d for 10 primes in geometric-arithmetic progression with the minimal sequence {1111^j + jd}, j = 0 to 9.

A209208 Values of the difference d for 9 primes in geometric-arithmetic progression with the minimal sequence {1111^j + jd}, j = 0 to 8.