A073425 a(0)=0; for n>0, a(n) = number of primes not exceeding n-th composite number.

0, 2, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 12, 12, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26

Offset

0,2

Comments

a(n-1) = A018252(n) - n. a(n-1) = inverse (frequency distribution) sequence of A014689(n), i.e. number of terms of sequence A014689(n) less than n. a(n) = A073169(n+1) - 1, for n >= 1. For n >= 1: a(n) + 1 = A073169(n) = the number of set {1, primes}, i.e. (A008578) less than (n)-th composite numbers (A002828(n)). a(n-1) = The number of primes (A000040(n)) less than n-th nonprime (A018252(n)). - Jaroslav Krizek, Jun 27 2009

Links

Table of n, a(n) for n=0..75.

Formula

a(n) = A000720(A002808(n)).

a(n) ~ n. - Charles R Greathouse IV, Sep 02 2015

Example

n=100: composite[100]=133,Pi[133]=32=a(100)

Mathematica

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[PrimePi[c[w]], {w, 1, 128}]
With[{nn=150}, PrimePi/@Complement[Range[nn], Prime[Range[PrimePi[nn]]]]] (* Harvey P. Dale, Jun 26 2013 *)

Crossrefs

Cf. A065890, A073426, A000720, A002808, A000040, A018252, A158611, A073169.

Sequence in context: A284359 A167991 A173073 * A087876 A006158 A340203

Adjacent sequences: A073422 A073423 A073424 * A073426 A073427 A073428

Keyword

nonn

Author

Labos Elemer, Jul 31 2002

Extensions

Edited by N. J. A. Sloane, Jul 04 2009 at the suggestion of R. J. Mathar

Correction for change of offset in A158611 and A008578 in Aug 2009 Jaroslav Krizek, Jan 27 2010

Status

approved