%I
%S 2,8,10,20,22,28,38,50,52,62,70,92,98,100,118,122,128,140,142,170,202,
%T 218,220,230,232,248,260,268,272,302,308,328,350,358,380,392,400,430,
%U 440,470,478,482,512,532,538,548,562,568,598,632,638,650,700,710,730
%N Values of the difference d for 3 primes in geometricarithmetic progression with the minimal sequence {3*3^j + j*d}, j = 0 to 2.
%C A geometricarithmetic progression of primes is a set of k primes (denoted by GAPk) 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 APk). The computations were done without any assumptions on the form of d. Primality requires d to be even and coprime to 3.
%H Sameen Ahmed Khan, <a href="/A209202/b209202.txt">Table of n, a(n) for n = 1..10000</a>
%H Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1203.2083">Primes in GeometricArithmetic Progression</a>, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).
%e d = 8 then {3*3^j + j*d}, j = 0 to 2, is {3, 17, 43}, which is 3 primes in geometricarithmetic progression.
%t p = 3; gapset3d = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d}] == {True, True, True}, AppendTo[gapset3d, d]], {d, 0, 1000, 2}]; gapset3d
%Y Cf. A172367, A209203, A209204, A209205, A209206, A209207, A209208, A209209, A209210.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Mar 06 2012
