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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 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 (list; graph; refs; listen; history; text; internal format)
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 A205791 A039696

Adjacent sequences:  A178990 A178991 A178992 * A178994 A178995 A178996

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jan 03 2011

STATUS

approved

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Last modified October 1 03:28 EDT 2020. Contains 337441 sequences. (Running on oeis4.)