A229989 - OEIS

A229989

Number of primes in the interval [floor(n/2), floor(3n/2)].

0, 2, 2, 3, 4, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 13, 14, 14, 14, 15, 16, 16, 16, 17, 18, 18, 18

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OFFSET

1,2

COMMENTS

Conjectures:

(1) a(n+1) - a(n) = 1 for infinitely many n;

(2) a(n+1) - a(n) = -1 for infinitely many n;

(3) a(n+1) - a(n) = -1 if and only if n = 2*prime(m+1) - 1.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5) = 4 counts the primes in the interval [2,7].