A178993 - OEIS

%I #12 Mar 05 2019 14:32:51

%S 1,2,3,4,4,6,7,7,8,8,6,12,12,13,15,16,16,18,18,19,17,16,20,21,18,21,

%T 25,23,26,30,30,31,28,32,34,34,36,36,38,38,39,41,41,43,43,43,42,45,41,

%U 48,46,48,50,45,52,55,55,54,48,60,56,61,56,60,64,64,66,66,61,67,66,66,68,72,66,67,76,76,72,73

%N Greatest k <= n such that 2^n+2^k+1 or 2^n+2^k-1 or 2^n-2^k+1 or 2^n-2^k-1 is prime

%C when k=n and 2^n+2^k-1 is prime then the prime is a Mersenne prime and n+1 is prime

%H Pierre CAMI, <a href="/A178993/b178993.txt">Table of n, a(n) for n = 1..5017</a>

%e 2^1+2^1+1=5 prime as 2^1+2^1-1=3 Mersenne prime so k(1)=1

%e 2^2+2^2-1=7 Mersenne prime so k(2)=2

%e 2^3+2^3+1=17 prime so k(3)=3

%e 2^4+2^4-1=31 Mersenne prime so k(4)=4

%e 2^5+2^4-1=47 prime so k(5)=4

%t f[n_] := Block[{k = n}, While[ !PrimeQ[2^n + 2^k + 1] && !PrimeQ[2^n + 2^k - 1] && !PrimeQ[2^n - 2^k + 1] && !PrimeQ[2^n - 2^k - 1], k--]; k]; Array[f, 80]

%t gk[n_]:=Module[{c=2^n,k=n},While[NoneTrue[{c+2^k+1,c+2^k-1,c-2^k+1,c-2^k- 1},PrimeQ],k--];k]; Array[gk,80] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 05 2019 *)

%K nonn

%O 1,2

%A _Pierre CAMI_, Jan 03 2011