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

1,1

Comments

Conjecture: a(n) >= 1. The length of interval I_n is n+2.

These intervals are considered in A307213.

Links

Table of n, a(n) for n=1..94.

Example

The intervals are I_1 = [1, 2, 3], I_2 = [4, 5, 6, 7], ...

Prog

(Magma) [#PrimesInInterval(Binomial(j+1, 2)+j-1, Binomial(j+1, 2)+2*j):j in [1..94]]; // Marius A. Burtea, Jul 13 2019

Crossrefs

Cf. A034856, A095998, A307213.

Sequence in context: A232551 A367006 A261129 * A305871 A089049 A275235

Adjacent sequences: A309118 A309119 A309120 * A309122 A309123 A309124

Keyword

nonn

Author

Wolfdieter Lang, Jul 13 2019

Status

approved