A309121 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.
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, 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, 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
Offset: 1
Keywords
Examples
The intervals are I_1 = [1, 2, 3], I_2 = [4, 5, 6, 7], ...
Programs
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Magma
[#PrimesInInterval(Binomial(j+1,2)+j-1,Binomial(j+1,2)+2*j):j in [1..94]]; // Marius A. Burtea, Jul 13 2019
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