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A159625 Numbers n such that 2^x + 3^y is never prime when max(x,y) = n 1
1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578, 7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749, 10735 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..18.

Underwood's posting in the PrimeNumbers list

Broadhurst's heuristic in the PrimeNumbers list

A list of 9983 primes or probable primes for the excluded cases with n < 10^4


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


Cf. A159270, A159266, A123359.

Sequence in context: A145755 A252300 A252442 * A156425 A247853 A093787

Adjacent sequences:  A159622 A159623 A159624 * A159626 A159627 A159628




David Broadhurst, Apr 17 2009


a(18) from Giovanni Resta, Apr 09 2014



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Last modified February 11 08:09 EST 2016. Contains 268163 sequences.