A075526 a(n) = A008578(n+2) - A008578(n+1).

1, 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, 10, 14, 4, 2, 4, 14, 6, 10, 2, 4, 6, 8, 6, 6, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6, 4, 6, 8, 4, 2, 4, 12, 8, 4, 8, 4, 6

Offset: 0

Author

Reinhard Zumkeller, Sep 22 2002

Keywords

• nonn

Comments

n appears this number of times in A000720. - Lekraj Beedassy, Jun 19 2006

a(0) = 1, for n >= 1: a(n) = differences between consecutive primes (A001223(n)) = A158611(n+2) - A158611(n+1). Partial sums give A006093 (shifted). - Jaroslav Krizek, Aug 04 2009

First differences of noncomposite numbers. - Juri-Stepan Gerasimov, Feb 17 2010

This is 1 together with A001223. A054541 is 2 together with A001223. A125266 is 3 together with A001223. - Omar E. Pol, Nov 01 2013

Crossrefs

Cf. A000040, A001223, A075527, A158611.

Programs

Mathematica

Prime[Range[100]] // Differences // Prepend[#, 1]& (* Jean-François Alcover, Dec 11 2021 *)

Formula

a(n) = A001223(n) for n>0.

Extensions

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