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%I #12 Mar 31 2012 10:28:59
%S 903030,1004250,3760290,7296450,7763520,17988210,28962390,29956950,
%T 33316320,37265160,39013800,39768150,43920480,50110620,54651480,
%U 56388810,74306610,74679810,75911850,89115210,92619690,98518800,108718080,116535300,116958450,117671820
%N 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.
%C 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.
%H Sameen Ahmed Khan, <a href="/A209208/b209208.txt">Table of n, a(n) for n = 1..539</a>
%H Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1203.2083/">Primes in Geometric-Arithmetic Progression</a>, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).
%e 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.
%t 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}]
%Y Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209209, A209210.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Mar 06 2012
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