A209206 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.

3324, 13260, 38064, 46260, 51810, 54510, 58914, 76050, 81510, 82434, 109800, 119340, 120714, 132390, 141480, 154254, 167904, 169734, 185040, 209214, 252864, 253110, 256080, 278514, 291930, 292314, 337104, 341694, 379944, 392964, 404730, 406074, 412050

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 to be multiple of 3# = 6 and coprime to 7.

Examples

			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.
		

Links

• Sameen Ahmed Khan, Table of n, a(n) for n = 1..5875
• Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).

Crossrefs

Cf. A172367, A209202, A209203, A209204, A209205, A209207, A209208, A209209, A209210.

Programs

Mathematica

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