Submitted to OEIS:

Numbers n such that 2^x + 3^y is never prime when max(x,y) = n

1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578,

7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749

Mark Underwood found that for each non-negative integer n < 1421

there is at least one prime of the form 2^m + 3^n or 2^n + 3^m

with m not exceeding n.

This sequence consists of numbers for which there is no such prime.

David Broadhurst estimated that a fraction in excess of 1/800

of the natural numbers belongs to this sequence and found

17 instances with n < 10^4.

For each of the remaining 9983 non-negative integers n < 10^4,

a prime or probable prime of the form 2^x + 3^y was found with

max(x,y) = n.

Each probable prime was subjected to a combination of

strong Fermat and strong Lucas tests.

http://physics.open.ac.uk/~dbroadhu/cert/marktest.txt
David Broadhurst, Apr 17 2009