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%I #9 Sep 08 2022 08:46:21
%S 2,2,1,2,2,2,2,2,3,3,2,3,4,2,3,4,3,4,3,4,5,4,4,3,5,5,4,6,5,5,3,5,7,7,
%T 4,5,7,4,7,6,6,6,7,7,8,5,6,6,11,4,5,9,8,8,9,7,8,7,8,7,9,7,11,6,9,9,11,
%U 9,7,7,11,11,10,9,8,9,7,11,9,12,9,12,11,11,10,10,10,12,11,13,9,10,11,12
%N a(n) gives the number of primes in the interval I_j = [(j^2 + 3*j - 2)/2, j*(j + 5)/2] = [A034856(j), A095998(j)], for j >= 1.
%C Conjecture: a(n) >= 1. The length of interval I_n is n+2.
%C These intervals are considered in A307213.
%e The intervals are I_1 = [1, 2, 3], I_2 = [4, 5, 6, 7], ...
%o (Magma) [#PrimesInInterval(Binomial(j+1,2)+j-1,Binomial(j+1,2)+2*j):j in [1..94]]; // _Marius A. Burtea_, Jul 13 2019
%Y Cf. A034856, A095998, A307213.
%K nonn
%O 1,1
%A _Wolfdieter Lang_, Jul 13 2019
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