This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A073425 #16 Oct 12 2024 09:07:24
%S A073425 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,
%T A073425 14,14,14,15,15,15,15,15,16,16,16,16,16,17,18,18,18,18,18,19,19,19,20,
%U A073425 21,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,24,25,25,25,26
%N A073425 a(0)=0; for n>0, a(n) = number of primes not exceeding n-th composite number.
%C A073425 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
%F A073425 a(n) = A000720(A002808(n)).
%F A073425 a(n) ~ n. - _Charles R Greathouse IV_, Sep 02 2015
%F A073425 a(n) = A002808(n)-n-1 for n > 0. - _Chai Wah Wu_, Oct 11 2024
%e A073425 n=100: composite[100]=133,Pi[133]=32=a(100)
%t A073425 c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[PrimePi[c[w]], {w, 1, 128}]
%t A073425 With[{nn=150},PrimePi/@Complement[Range[nn],Prime[Range[PrimePi[nn]]]]] (* _Harvey P. Dale_, Jun 26 2013 *)
%o A073425 (Python)
%o A073425 from sympy import composite
%o A073425 def A073425(n): return composite(n)-n-1 if n else 0 # _Chai Wah Wu_, Oct 11 2024
%Y A073425 Cf. A065890, A073426, A000720, A002808, A000040, A018252, A158611, A073169.
%K A073425 nonn
%O A073425 0,2
%A A073425 _Labos Elemer_, Jul 31 2002
%E A073425 Edited by _N. J. A. Sloane_, Jul 04 2009 at the suggestion of R. J. Mathar
%E A073425 Correction for change of offset in A158611 and A008578 in Aug 2009 _Jaroslav Krizek_, Jan 27 2010