# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a159625 Showing 1-1 of 1 %I A159625 #16 Aug 06 2022 07:23:55 %S A159625 1679,1743,4980,4982,5314,5513,5695,6100,6578,7251,7406,7642,8218, %T A159625 8331,9475,9578,9749,10735 %N A159625 Numbers n such that 2^x + 3^y is never prime when max(x,y) = n %C A159625 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. %C A159625 This sequence consists of numbers for which there is no such prime. %C A159625 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. %C A159625 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. %C A159625 Each probable prime was subjected to a combination of strong Fermat and strong Lucas tests. %H A159625 Broadhurst's heuristic in the PrimeNumbers list. [Broken link] %H A159625 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] %H A159625 Underwood's posting in the PrimeNumbers list %H A159625 A list of 9983 primes or probable primes for the excluded cases with n < 10^4 %e A159625 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. %Y A159625 Cf. A159270, A159266, A123359. %K A159625 nonn,more,hard %O A159625 1,1 %A A159625 _David Broadhurst_, Apr 17 2009 %E A159625 a(18) from _Giovanni Resta_, Apr 09 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE