A076806 Minimal odd k such that k*2^n-1 and k*2^n+1 are twin primes.

3, 1, 9, 15, 81, 3, 9, 57, 45, 15, 99, 165, 369, 45, 345, 117, 381, 3, 69, 447, 81, 33, 1179, 243, 765, 375, 81, 387, 45, 345, 681, 585, 375, 267, 741, 213, 429, 3093, 165, 267, 255, 1095, 9, 147, 849, 405, 1491, 177, 1941, 927, 1125, 1197, 2001, 333, 519

Offset: 1

Author

Andrey V. Kulsha, Nov 18 2002

Keywords

• nonn

Examples

			a(4)=15 because k*2^4-1 and k*2^4+1 are twin primes for k=15 and are not twin primes for smaller odd k.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..16999 (first 200 terms from Harvey P. Dale, terms extracted from rieselprime link)
• A. V. Kulsha, k*2^n-1 and k*2^n+1 are twins, provides terms for n<=1000.
• Andrey Kulsha and others, k*2^n-1 and k*2^n+1 are twins, digest of 15 messages in primenumbers Yahoo group, Nov 18, 2002 - May 23, 2005.
• Author?, First odd k for which k*2^n-1 k*2^n+1 are twins, provides terms for n<=17000.

Crossrefs

Cf. A063983.

Programs

Magma

a:=[]; for n in [1..55] do k:=1; while not (IsPrime(k*2^n-1) and IsPrime(k*2^n+1)) do k:=k+2; end while; Append(~a,k); end for; a; // Marius A. Burtea, Nov 16 2019

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[k*2^n - 1] || !PrimeQ[k*2^n + 1], k += 2]; k]; Array[f, 50]
mok[n_]:=Module[{n2=2^n,k=1},While[!AllTrue[k*n2+{1,-1},PrimeQ],k=k+2];k]; Array[mok,60] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 19 2015 *)

PARI

for(n=1, 100, N=2^n; forstep(k=1, 10^100, 2, if(isprime(k*N-1) && isprime(k*N+1), print1(k, ", "); break)))

Sage

A076806 = lambda n: next(k for k in IntegerRange(1, infinity, 2) if is_prime(k*2**n-1) and is_prime(k*2**n+1)) # D. S. McNeil, Dec 08 2010