A209204 Values of the difference d for 5 primes in geometric-arithmetic progression with the minimal sequence {5*5^j + j*d}, j = 0 to 4.

84, 114, 138, 168, 258, 324, 348, 462, 552, 588, 684, 714, 744, 798, 882, 894, 972, 1176, 1602, 1734, 2196, 2256, 2442, 2478, 2568, 2646, 2658, 2688, 3036, 3162, 3444, 3906, 4524, 5154, 5406, 5544, 5766, 5796, 6018, 6456, 6594, 6636, 6936, 7272, 7938, 8736

Offset: 1

Author

Sameen Ahmed Khan, Mar 06 2012

Keywords

• nonn

Comments

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 3# = 6 and coprime to 5.

Subsequence of A209203. - Zak Seidov, Jul 06 2013

Examples

			d = 114 then {5*5^j + j*d}, j = 0 to 4, is {5, 139, 353, 967, 3581}, which is 5 primes in geometric-arithmetic progression.
		

Links

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

Crossrefs

Cf. A172367, A209202, A209203, A209205, A209206, A209207, A209208, A209209, A209210.

Programs

Mathematica

p = 5; gapset5d  = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d, p*p^3 + 3*d, p*p^4 + 4*d}] == {True, True, True, True, True}, AppendTo[gapset5d, d]], {d, 2, 10000, 2}]; gapset5d