A263046 Smallest number k>2 such that k*2^n + 1 is a prime number.

4, 3, 3, 5, 6, 3, 3, 5, 3, 15, 12, 6, 3, 5, 4, 5, 12, 6, 3, 11, 7, 11, 25, 20, 10, 5, 7, 15, 12, 6, 3, 35, 18, 9, 12, 6, 3, 15, 10, 5, 6, 3, 9, 9, 15, 35, 19, 27, 15, 14, 7, 14, 7, 20, 10, 5, 27, 29, 54, 27, 31, 36, 18, 9, 12, 6, 3, 9, 31, 23, 39, 39, 40, 20, 10, 5, 58

Offset: 0

Author

Pierre CAMI, Oct 08 2015

Keywords

• nonn

Comments

If k = 2^j then 2^(n+j) + 1 is a Fermat prime.

a(n) = 3 if and only if 3*2^n + 1 is a prime; that is, n belongs to A002253. - Altug Alkan, Oct 08 2015

a(n+1) >= ceiling(a(n)/2). If a(n) is even then a(n+1) = a(n)/2. - Robert Israel, Oct 08 2015

Examples

			3*2^1 + 1 = 7 (prime), so a(1)=3:
3*2^2 + 1 = 13 (prime), so a(2)=3;
3*2^3 + 1 = 25 (composite), 4*2^3 + 1 = 33 (composite), 5*2^3 - 1 = 41 (prime), so a(3)=5.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A247479, A262994.

Programs

Maple

f:= proc(n) local k;
    for k from 3 do if isprime(k*2^n+1) then return k fi od
  end proc:
seq(f(n),n=1..100); # Robert Israel, Oct 08 2015

Mathematica

Table[k = 3; While[! PrimeQ[k 2^n + 1], k++]; k, {n, 76}] (* Michael De Vlieger, Oct 08 2015 *)

PARI

a(n) = {k=3; while (! isprime(k*2^n+1), k++); k;} \\ Michel Marcus, Oct 08 2015