A073168 -id:A073168 - cp's OEIS frontend

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

Labos Elemer, Jul 19 2002

nonn

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]

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

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

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 *)

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

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

A073170 a(1) = a(2) = 0; for n>2, a(n) = prime(n-1)-n+1.

Original entry on oeis.org

0, 0, 1, 2, 3, 6, 7, 10, 11, 14, 19, 20, 25, 28, 29, 32, 37, 42, 43, 48, 51, 52, 57, 60, 65, 72, 75, 76, 79, 80, 83, 96, 99, 104, 105, 114, 115, 120, 125, 128, 133, 138, 139, 148, 149, 152, 153, 164, 175, 178, 179, 182, 187, 188, 197, 202, 207, 212, 213, 218, 221

Offset: 1

Labos Elemer, Jul 19 2002

nonn

Smallest x such that A002808(x)-x (cf. A073169) equals n, or 0 if no such value exists.

Cf. A002808, A073168, A073169. Essentially same sequence as A014689.

Cf. A000040, A014689.

f[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] t=Table[0, {100}]; Do[s=f[n]-n; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10000}]; t
Join[{0,0},Table[Prime[n-1]-n+1,{n,3,70}]] (* Harvey P. Dale, Dec 18 2012 *)

a(n)=Min{x; composite[x]-x=n}

Simpler description from Vladeta Jovovic, Mar 29 2003

Definition corrected by Harvey P. Dale, Dec 18 2012

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions