A134855 Least odd prime p such that 1 + p*2^n is also prime.

3, 3, 5, 7, 3, 3, 5, 3, 23, 13, 29, 3, 5, 7, 5, 37, 53, 3, 11, 7, 11, 37, 71, 73, 5, 7, 17, 13, 23, 3, 239, 43, 113, 163, 59, 3, 89, 349, 5, 97, 3, 73, 11, 67, 101, 19, 101, 61, 23, 7, 17, 7, 233, 127, 5, 541, 29, 103, 71, 31, 53, 109, 179, 163, 71, 3, 929, 31, 23, 193, 101, 127

Offset: 1

Author

T. D. Noe, Nov 13 2007

Keywords

• nonn

Comments

Let q = 1 + a(n)*2^n. Then q is least prime such that A098006(pi(q)) = 2^(n-1). See A134854 for the values of q.

a(n) = prime(k) for some k < 5*n for n <= 10000 . - Pierre CAMI, Jul 20 2014

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe)

Crossrefs

Cf. A098006, A134854.

Programs

Mathematica

Table[Select[Prime[Range[2,10000]], PrimeQ[1+2^k # ]&, 1][[1]], {k,100}]
lop[n_]:=Module[{k=3,c=2^n},While[!PrimeQ[1+k*c],k=NextPrime[k]];k]; Array[ lop,80] (* Harvey P. Dale, Sep 01 2022 *)

PARI

a(n) = p=3; t=2^n; while(!isprime(1+p*t), p=nextprime(p+1)); p \\ Colin Barker, Jul 22 2014