A079952 Number of primes less than prime(n)/2.

0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 13, 14, 15, 15, 15, 16, 16, 16, 18, 18, 19, 19, 21, 21, 21, 22, 23, 23, 24, 24, 24, 24, 25, 25, 27, 29, 30, 30, 30, 30, 30, 30, 31, 32, 32, 32, 33, 34, 34, 34, 36, 36, 36, 37, 38, 39, 40

Offset: 1

Author

Reinhard Zumkeller, Jan 19 2003

Keywords

• nonn

Comments

Previous name: Number of primes p such that prime(n) mod 2*p < prime(n).

Same as A055930, except for a(2). [Noticed by R. J. Mathar, Dec 15 2008, proved by Andrey Zabolotskiy, Oct 26 2017]

Examples

			n = 6: prime(6) = 13 and 2, 3, 5 are less than 13/2, therefore a(6) = 3.
		

Crossrefs

Cf. A000040, A000720, A055377, A055930, A079951, A079953, A217564.

Programs

Mathematica

Table[PrimePi[Prime[n]/2], {n, 75}] (* Michael De Vlieger, Sep 20 2017 *)

PARI

a(n) = primepi(prime(n)/2); \\ Michel Marcus, Sep 20 2017

Formula

A079950(n, a(n) + 1) = prime(n).

Where defined, that is for n > 2, prime(a(n)) = A055377(prime(n)). - Peter Munn, Sep 18 2017

0 with partial sums of A217564. - David A. Corneth, Oct 26 2017 (found earlier by Peter Munn).

Extensions

New name from Peter Munn, Sep 18 2017