A230699 Sequence of pairs k,g such that k*2^n-1, k*2^n-1+g, k*2^n-1+2*g, and k*2^n+3*g are four consecutive primes in arithmetic progression for the smallest odd k.

135, -6, 63, 6, 415, -6, 987, 6, 55, -6, 273, 6, 1195, -6, 299, 18, 1371, 6, 5, -6, 189, 6, 1077, 6, 7111, 6, 15, -6, 2821, -18, 15465, 24, 1081, 6, 11475, -6, 17155, -6, 3393, 12, 9751, 6, 16523, -24, 165, -6, 7395, -6, 8695, -6, 20325, -6, 7153, 18, 2235, -6

Offset

1,1

Comments

The number g may be negative.

g is always 0 mod 6 so a multiple of 6.

Links

Pierre CAMI, Table of n, a(n) for n = 1..390

Example

135*2^1-1=269, 135*2^1-1-6=263, 135*2^1-1-2*6=257, 135*2^1-1-3*6=251
269, 263, 257, 251 are four consecutive primes in arithmetic progression so a(1)=135, a(2)=-6.
63*2^2-1=251, 63*2^2-1+6=257, 63*2^2-1+2*6=263, 63*2^2-1-3*6=269
251, 257, 263, 269 are four consecutive primes in arithmetic progression so a(3)=63 a(4)=6.

Crossrefs

Cf. A227888, A228452, A228754.

Sequence in context: A007251 A219443 A348815 * A335950 A355002 A038369

Adjacent sequences: A230696 A230697 A230698 * A230700 A230701 A230702

Keyword

sign

Author

Pierre CAMI, Oct 30 2013

Status

approved