A049711 a(n) = n - prevprime(n).

1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

Comments

All runs end in even numbers at a(p), new highs are found at A000101 and the increasing gap size is A005250. - Robert G. Wilson v, Dec 07 2001

All terms are positive since here the variant 2 (A151799(n) < n) of the prevprime function is used, rather than the variant 1 (A007917(n) <= n). - M. F. Hasler, Sep 09 2015

Crossrefs

Cf. A000101, A005250, A049613, A049653, A049716, A049847, A064722.

Cf. A151799, A007917.

Cf. A175851.

Programs

Maple

A049711 := n-> n-prevprime(n);

Mathematica

PrevPrim[n_] := Block[ {k = n - 1}, While[ !PrimeQ[k], k-- ]; Return[k]]; Table[ n - PrevPrim[n], {n, 3, 100} ]
Array[#-NextPrime[#,-1]&,100,3] (* Harvey P. Dale, Dec 07 2011 *)

PARI

A049711(n)=n-precprime(n-1) \\ M. F. Hasler, Sep 09 2015

Formula

a(n) = A064722(n-1) + 1. - Pontus von Brömssen, Jul 31 2022