

A079952


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


5



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
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OFFSET

1,4


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]


LINKS

Table of n, a(n) for n=1..69.


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).


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A000040, A000720, A055377, A055930, A079951, A079953, A217564.
Sequence in context: A057355 A171975 A160511 * A055930 A090638 A247908
Adjacent sequences: A079949 A079950 A079951 * A079953 A079954 A079955


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jan 19 2003


EXTENSIONS

New name from Peter Munn, Sep 18 2017


STATUS

approved



