A230699 - OEIS

%I #21 Nov 01 2013 14:23:43

%S 135,-6,63,6,415,-6,987,6,55,-6,273,6,1195,-6,299,18,1371,6,5,-6,189,

%T 6,1077,6,7111,6,15,-6,2821,-18,15465,24,1081,6,11475,-6,17155,-6,

%U 3393,12,9751,6,16523,-24,165,-6,7395,-6,8695,-6,20325,-6,7153,18,2235,-6

%N 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.

%C The number g may be negative.

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

%H Pierre CAMI, <a href="/A230699/b230699.txt">Table of n, a(n) for n = 1..390</a>

%e 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

%e 269, 263, 257, 251 are four consecutive primes in arithmetic progression so a(1)=135, a(2)=-6.

%e 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

%e 251, 257, 263, 269 are four consecutive primes in arithmetic progression so a(3)=63 a(4)=6.

%Y Cf. A227888, A228452, A228754.

%K sign

%O 1,1

%A _Pierre CAMI_, Oct 30 2013