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.

81647160420, 170655787050, 211212209880, 227961624450

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..4.

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A034653 A289116 A249621 * A172548 A172611 A172716

Adjacent sequences: A227277 A227278 A227279 * A227281 A227282 A227283

Keyword

nonn

Author

Sameen Ahmed Khan, Jul 05 2013

Status

approved