%I #16 Aug 06 2022 07:23:55

%S 1679,1743,4980,4982,5314,5513,5695,6100,6578,7251,7406,7642,8218,

%T 8331,9475,9578,9749,10735

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

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

%C 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 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 Each probable prime was subjected to a combination of strong Fermat and strong Lucas tests.

%H Broadhurst's <a href="http://groups.yahoo.com/group/primenumbers/message/20062">heuristic</a> in the PrimeNumbers list. [Broken link]

%H Maximilian Hasler, Mike Oakes, Mark Underwood, David Broadhurst and others, <a href="/A159625/a159625.txt">Primes of the form (x+1)^p-x^p</a>, digest of 22 messages in primenumbers Yahoo group, Apr 5 - May 7, 2009. [Cached copy]

%H Underwood's <a href="http://groups.yahoo.com/group/primenumbers/message/20029">posting</a> in the PrimeNumbers list

%H A list of <a href="http://physics.open.ac.uk/~dbroadhu/cert/marktest.txt">9983</a> primes or probable primes for the excluded cases with n < 10^4

%e 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 Cf. A159270, A159266, A123359.

%K nonn,more,hard

%O 1,1

%A _David Broadhurst_, Apr 17 2009

%E a(18) from _Giovanni Resta_, Apr 09 2014