A192451 Number of primes between successive hexagonal numbers.

0, 3, 3, 3, 5, 4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 8, 12, 12, 11, 12, 11, 14, 14, 12, 16, 10, 16, 17, 15, 16, 15, 19, 14, 20, 16, 19, 20, 18, 15, 21, 20, 23, 21, 21, 22, 22, 21, 23, 21, 25, 22, 26, 23, 26, 25, 28, 23, 28, 27, 24

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = A000720(A000384(n)) - A000720(A000384(n-1)).

Example

There are no primes between 0 and 1, so a(1) = 0;
there are three primes between 1 and 6, so a(2) = 3;
there are three primes between 6 and 15, so a(3) = 3.

Maple

A192451 := proc(n) numtheory[pi](n*(2*n-1)) -numtheory[pi]((n-1)*(2*n-3)) ; end proc: # R. J. Mathar, Jul 01 2011

Prog

(PARI) a(n)=sum(k=2*n^2-5*n+4, n*(2*n-1), isprime(k)) \\ Charles R Greathouse IV, Jul 13 2011

Crossrefs

Cf. A000384, A000720.

Sequence in context: A076566 A083574 A108025 * A129856 A136800 A126661

Adjacent sequences: A192448 A192449 A192450 * A192452 A192453 A192454

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 01 2011

Extensions

Corrected by R. J. Mathar, Jul 01 2011

Status

approved