A073169 a(n)=A002808(n)-n, difference between n-th composite and n.

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

Offset: 1

Author

Labos Elemer, Jul 19 2002

Keywords

• nonn

Comments

a(n) = the number of numbers of set {1, prime} (A008578(n)) less than n-th composite numbers (A002808(n)). a(n) = inverse (frequency distribution) sequence of A162177(n), i.e. number of terms of sequence A162177(n) less than n for n >= 1. a(n) = A002808(n) + A162177(n) - A158611(n+1) for n >= 1. a(n) = A002808(n) + A162177(n) - A008578(n) for n >= 1. [From Jaroslav Krizek, Jul 23 2009]

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007821, A022449, A000040, A002808, A073168.

Programs

Mathematica

c[n_Integer] := FixedPoint[n+PrimePi[ # ]+1&, n] Table[c[w]-w, {w, 1, 128}]
With[{c=Select[Range[100],CompositeQ]},#[[1]]-#[[2]]&/@Thread[ {c,Range[ Length[ c]]}]] (* Harvey P. Dale, Feb 03 2015 *)

Formula

a(n)=1+A073425(n). [From R. J. Mathar, Jul 31 2009]

Extensions

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