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

1,1

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)

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 *)

Prog

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

Crossrefs

Cf. A098006, A134854.

Sequence in context: A092035 A164914 A247479 * A335045 A110246 A070543

Adjacent sequences: A134852 A134853 A134854 * A134856 A134857 A134858

Keyword

nonn

Author

T. D. Noe, Nov 13 2007

Status

approved