A209208 Values of the difference d for 9 primes in geometric-arithmetic progression with the minimal sequence {11*11^j + j*d}, j = 0 to 8.

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

Author

Sameen Ahmed Khan, Mar 06 2012

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• 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).

Crossrefs

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

Programs

Mathematica

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}]