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A209202 Values of the difference d for 3 primes in geometric-arithmetic progression with the minimal sequence {3*3^j + j*d}, j = 0 to 2. 10

%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 geometric-arithmetic progression with the minimal sequence {3*3^j + j*d}, j = 0 to 2.

%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 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 Geometric-Arithmetic 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 geometric-arithmetic 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

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)