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%I #15 Oct 06 2013 14:29:03
%S 2,1,1,2,2,1,2,3,2,2,3,3,3,3,2,4,3,3,4,4,4,4,4,4,4,4,5,5,6,4,5,3,6,6,
%T 7,5,5,6,4,8,5,6,6,8,6,8,5,7,5,11,4,6,9,7,8,9,8,7,7,9,7,8,7,12,5,9,9,
%U 11,9,7,7,12,10,10,9,9,9,6,11,10,11,9,12,11,12,9,10,11,12,10,13,9,11,10
%N Number of primes between n(n+1)/2 (exclusive) and (n+1)(n+2)/2 (inclusive).
%C Inspired by the weaker Legendre conjecture that there should be at least one prime between n^2 and (n+1)^2.
%H T. D. Noe, <a href="/A065382/b065382.txt">Table of n, a(n) for n = 1..10000</a>
%e a(10) = 2 because between 10*(10+1)/2=55 and (10+1)*(10+2)/2=66 there are 2 primes: 59, 61.
%t Table[ PrimePi[n(n + 1)/2] - PrimePi[n(n - 1)/2], {n, 2, 96}]
%Y A000217, A014085, A065383, A065384.
%Y Essentially the same as A066888 and A090970.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Nov 05 2001
%E Definition improved by _Robert G. Wilson v_, Apr 22 2003
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