A159269 - OEIS

%I #6 Apr 06 2014 08:04:50

%S 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,

%T 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,

%U 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

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

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

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

%e a(0)=1 since 2^1+3^0=3 is prime.

%e a(1)=1 since 2^1+3^1=5 is prime.

%e a(2)=1 since 2^2+3^1=7, or 2^1+3^2=11, is prime. (Only one prime is required).

%e a(3)=1 since 2^3+3^1=11 and also 2^1+3^3=29, are prime.

%e a(4)=1 since 2^4+3^1=19 (and also 2^1+3^4=83) are prime.

%e 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.

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

%K nonn

%O 0,6

%A _M. F. Hasler_, Apr 08 2009