

A178993


Greatest k <= n such that 2^n+2^k+1 or 2^n+2^k1 or 2^n2^k+1 or 2^n2^k1 is prime


4



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
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OFFSET

1,2


COMMENTS

when k=n and 2^n+2^k1 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+2^11=3 Mersenne prime so k(1)=1
2^2+2^21=7 Mersenne prime so k(2)=2
2^3+2^3+1=17 prime so k(3)=3
2^4+2^41=31 Mersenne prime so k(4)=4
2^5+2^41=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^k1, c2^k+1, c2^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 A205791 A039696
Adjacent sequences: A178990 A178991 A178992 * A178994 A178995 A178996


KEYWORD

nonn


AUTHOR

Pierre CAMI, Jan 03 2011


STATUS

approved



