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A073425
a(0)=0; for n>0, a(n) = number of primes not exceeding n-th composite number.
13
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
FORMULA
a(n) = A000720(A002808(n)).
a(n) ~ n. - Charles R Greathouse IV, Sep 02 2015
a(n) = A002808(n)-n-1 for n > 0. - Chai Wah Wu, Oct 11 2024
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 *)
PROG
(Python)
from sympy import composite
def A073425(n): return composite(n)-n-1 if n else 0 # Chai Wah Wu, Oct 11 2024
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