A209207 Values of the difference d for 8 primes in geometric-arithmetic progression with the minimal sequence {11*11^j + j*d}, j = 0 to 7.

62610, 165270, 420300, 505980, 669780, 903030, 932400, 1004250, 1052610, 1093080, 1230270, 1231020, 1248120, 1433250, 1571430, 1742040, 1908480, 2668290, 2885220, 3367590, 3416520, 3760290, 3813630, 3965250, 3995340, 4137450, 4334610, 5443620, 5939250

Offset

1,1

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 5# = 30 and coprime to 11.

Links

Sameen Ahmed Khan, Table of n, a(n) for n = 1..3233

Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).

Example

d = 165270 then {11*11^j + j*d}, j = 0 to 8, is {11, 165391, 331871, 510451, 822131, 2597911, 20478791, 215515771}, which is 8 primes in geometric-arithmetic progression.

Mathematica

p = 11; gapset8d = {}; 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, p*p^7 + 7*d}] == {True, True, True, True, True, True, True, True}, AppendTo[gapset8d, d]], {d, 0, 10^7, 2}]

Crossrefs

Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209208, A209209, A209210.

Sequence in context: A257157 A254739 A205764 * A224649 A253854 A237675

Adjacent sequences: A209204 A209205 A209206 * A209208 A209209 A209210

Keyword

nonn

Author

Sameen Ahmed Khan, Mar 06 2012

Status

approved