

A209202


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


10



2, 8, 10, 20, 22, 28, 38, 50, 52, 62, 70, 92, 98, 100, 118, 122, 128, 140, 142, 170, 202, 218, 220, 230, 232, 248, 260, 268, 272, 302, 308, 328, 350, 358, 380, 392, 400, 430, 440, 470, 478, 482, 512, 532, 538, 548, 562, 568, 598, 632, 638, 650, 700, 710, 730
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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.


LINKS

Sameen Ahmed Khan, Table of n, a(n) for n = 1..10000
Sameen Ahmed Khan, Primes in GeometricArithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).


EXAMPLE

d = 8 then {3*3^j + j*d}, j = 0 to 2, is {3, 17, 43}, which is 3 primes in geometricarithmetic progression.


MATHEMATICA

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


CROSSREFS

Cf. A172367, A209203, A209204, A209205, A209206, A209207, A209208, A209209, A209210.
Sequence in context: A082396 A195582 A071388 * A032356 A114272 A193266
Adjacent sequences: A209199 A209200 A209201 * A209203 A209204 A209205


KEYWORD

nonn


AUTHOR

Sameen Ahmed Khan, Mar 06 2012


STATUS

approved



