A123340 Least m such that 2^n+3^m is prime.

0, 0, 0, 1, 0, 2, 1, 1, 0, 2, 2, 4, 1, 3, 3, 1, 0, 8, 1, 4, 8, 8, 6, 2, 7, 27, 6, 13, 1, 10, 1, 6, 4, 8, 18, 9, 19, 2, 15, 29, 3, 3, 17, 10, 3, 11, 6, 2, 5, 20, 34, 4, 12, 10, 26, 1, 4, 2, 9, 29, 29, 10, 34, 13, 4, 8, 2, 1, 8, 10, 26, 50, 19, 12, 10, 8, 13, 27, 17, 9, 33, 4, 2, 17, 1, 7, 3, 5, 61, 26

Offset: 0

Author

Zak Seidov, Oct 11 2006

Keywords

• nonn

Examples

			a(0)=0 because 2^0+3^0=1+1=2 is prime,
a(3)=1 because 2^3+3^1=8+3=11 is prime,
a(17)=8 because 2^17+3^8=131072+6561=137633 is prime,
a(25)=27 because 33554432+7625597484987=7625631039419 is prime, etc.
		

Programs

Mathematica

a[n_] := Module[{m, t = 2^n}, For[m = 0, True, m++, If[PrimeQ[t + 3^m], Return[m]]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 01 2023 *)