OFFSET
1,1
COMMENTS
Mark Underwood found that for each nonnegative 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 nonnegative 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.
LINKS
Broadhurst's heuristic in the PrimeNumbers list. [Broken link]
Maximilian Hasler, Mike Oakes, Mark Underwood, David Broadhurst and others, Primes of the form (x+1)^p-x^p, digest of 22 messages in primenumbers Yahoo group, Apr 5 - May 7, 2009. [Cached copy]
Underwood's posting in the PrimeNumbers list
A list of 9983 primes or probable primes for the excluded cases with n < 10^4
EXAMPLE
a(3) = 4980, since there is no prime of the form 2^m + 3^4980 or 2^4980 + 3^m with m < 4981 and 4980 is the third number n such that 2^x + 3^y is never prime when max(x,y) = n.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
David Broadhurst, Apr 17 2009
EXTENSIONS
a(18) from Giovanni Resta, Apr 09 2014
STATUS
approved