A159269 Least positive integer such that 2^m+3^n or 2^n+3^m is prime.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 3, 1, 1, 1, 6, 1, 4, 3, 8, 2, 2, 1, 7, 1, 4, 1, 10, 1, 4, 4, 8, 15, 6, 1, 2, 3, 8, 3, 3, 2, 6, 3, 11, 6, 2, 5, 4, 18, 4, 12, 6, 26, 1, 4, 2, 9, 6, 4, 10, 18, 1, 4, 6, 2, 1, 8, 10, 26, 12, 17, 12, 10, 4, 13, 3, 7, 9, 11, 4, 2, 17, 1, 7, 3, 2, 3, 26, 22, 6, 12, 8, 9

Offset: 0

Author

M. F. Hasler, Apr 08 2009

Keywords

• nonn

Comments

It seems that a(n)<=n for all n>0.

Examples

			a(0)=1 since 2^1+3^0=3 is prime.
a(1)=1 since 2^1+3^1=5 is prime.
a(2)=1 since 2^2+3^1=7, or 2^1+3^2=11, is prime. (Only one prime is required).
a(3)=1 since 2^3+3^1=11 and also 2^1+3^3=29, are prime.
a(4)=1 since 2^4+3^1=19 (and also 2^1+3^4=83) are prime.
a(5)=2 is the least integer m such that 2^5+3^m (=41) is prime and 2^m+3^5 is not prime until A159267(5)=4.
		

Programs

PARI

A159269(n,m=0)=until( is/*pseudo*/prime(2^n+3^m++) || is/*pseudo*/prime(3^n+2^m),);m

Formula

a(n) = min { A123359(n), A159266(n) }