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%I #12 Mar 31 2012 10:28:59
%S 903030,17988210,28962390,39768150,74306610,89115210,116535300,
%T 173227980,186013380,237952050,359613030,386317920,392253990,
%U 443687580,499153200,548024610,591655080,652133160,665780640,705583830,758828310,910046550,920546160,921847290
%N Values of the difference d for 10 primes in geometric-arithmetic progression with the minimal sequence {11*11^j + j*d}, j = 0 to 9.
%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="/A209209/b209209.txt">Table of n, a(n) for n = 1..96</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 = 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.
%t 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}]
%Y Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209208, A209210.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Mar 06 2012
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