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

1,1

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A064007 A358127 A068568 * A166268 A239669 A185220

Adjacent sequences: A073166 A073167 A073168 * A073170 A073171 A073172

Keyword

nonn

Author

Labos Elemer, Jul 19 2002

Extensions

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

Status

approved