A178993 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

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

Offset

1,2

Comments

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

Links

Pierre CAMI, Table of n, a(n) for n = 1..5017

Example

2^1+2^1+1=5 prime as 2^1+2^1-1=3 Mersenne prime so k(1)=1
2^2+2^2-1=7 Mersenne prime so k(2)=2
2^3+2^3+1=17 prime so k(3)=3
2^4+2^4-1=31 Mersenne prime so k(4)=4
2^5+2^4-1=47 prime so k(5)=4

Mathematica

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]
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 *)

Crossrefs

Sequence in context: A066981 A130043 A089266 * A193768 A361784 A361318

Adjacent sequences: A178990 A178991 A178992 * A178994 A178995 A178996

Keyword

nonn

Author

Pierre CAMI, Jan 03 2011

Status

approved