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%I #12 Mar 31 2012 10:28:59
%S 3324,13260,38064,46260,51810,54510,58914,76050,81510,82434,109800,
%T 119340,120714,132390,141480,154254,167904,169734,185040,209214,
%U 252864,253110,256080,278514,291930,292314,337104,341694,379944,392964,404730,406074,412050
%N Values of the difference d for 7 primes in geometric-arithmetic progression with the minimal sequence {7*7^j + j*d}, j = 0 to 6.
%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 to be multiple of 3# = 6 and coprime to 7.
%H Sameen Ahmed Khan, <a href="/A209206/b209206.txt">Table of n, a(n) for n = 1..5875</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 = 13260 then {7*7^j + j*d}, j = 0 to 6, is {7, 13309, 26863, 42181, 69847, 183949, 903103}, which is 7 primes in geometric-arithmetic progression.
%t p = 7; gapset7d = {}; 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}] == {True, True, True, True, True, True, True}, AppendTo[gapset7d, d]], {d, 0, 500000, 2}]; gapset7d
%Y Cf. A172367, A209202, A209203, A209204, A209205, A209207, A209208, A209209, A209210.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Mar 06 2012
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