A260350 Define g(k) = min(n: n >= 0, 2^n + k prime). Then a(n) = min(odd k: g(k) = n).

1, 3, 7, 23, 31, 47, 199, 83, 61, 257, 139, 953, 991, 647, 1735, 383, 511, 1337, 1069, 713, 271, 1937, 3223, 5213, 751, 8477, 4339, 353, 1501, 287, 829, 1553, 2371, 1811, 11185, 3023, 7381, 7937, 6439, 1433, 13975, 2897, 4183

Offset: 0

Author

Hugo van der Sanden, Jul 23 2015

Keywords

• nonn

Comments

Previous name: a(n) = min(k : A067760((k-1)/2)) = n.

a(n) is the first odd number k for which 2^m + k is the first prime value, as m ranges from 0 to n, or 0 if no such k exists. Thus it is the first k for which A067760((k-1)/2) = n, and therefore also the first k for which you need to test primality of exactly n values to show that it is not a dual Sierpiński number.

In the name, g(n) = A067760(n) except for n=1. - Michel Marcus, Apr 07 2018

Examples

			2^i + 7 is composite for i < 2 (with values 8, 9) but prime for i = 2 (11); the smaller odd numbers 1, 3 and 5 each yield a prime for smaller i, so a(2) = 7.
		

Links

• Hugo van der Sanden, Table of n, a(n) for n = 0..1087

Crossrefs

Cf. A067760, A076336, A260349.

Programs

PARI

g(k) = {my(j=0); while (!isprime(2^j+k), j++); j;}
a(n) = {my(k = 1); while(g(k) != n, k+=2); k;} \\ Michel Marcus, Apr 07 2018

Formula

For n>=2, a(n) = (min(k : A067760((k-1)/2)) = n). - Michel Marcus, Apr 07 2018

Extensions

New name from Hugo van der Sanden and Michel Marcus, Apr 07 2018