%I #7 May 27 2017 03:00:14
%S 1,1,3,2,3,2,2,3,1,1,3,1,2,2,1,1,2,2,1,3,1,1,3,1,1,1,0,1,2,2,2,2,1,0,
%T 2,1,2,2,1,0,3,1,2,2,0,1,1,2,0,2,1,1,3,2,1,2,0,1,1,1,1,1,1,0,2,0,2,2,
%U 1,1,2,1,1,2,1,1,1,1,1,2,1,0,3,1,1,1,0,1,2,2,1,1,0,0,1,1,2,3,1,1,2,1,1,1,1
%N Number of times primes can be produced by taking the absolute difference between the n-th triangular number and another triangular number.
%F a(n) =A056562(n)+A056563(n) =number of primes (with multiplicity) in {m, m+1, 2m-1, 2m+3}
%e a(2)=3 because 2nd triangular number is 3 and all three of 3-0=3, 3-1=2 and 6-3=3 are prime [n=2 is the only case where there is multiplicity].
%Y Cf. A000217, A001227, A056562, A056563
%K nonn
%O 0,3
%A _Henry Bottomley_, Jun 27 2000