A242746 Least k > 0 such that (k!+n!)/(k+n) is an integer.

1, 1, 3, 1, 4, 1, 5, 3, 6, 1, 7, 1, 7, 6, 5, 1, 7, 1, 5, 4, 7, 1, 7, 6, 4, 9, 8, 1, 7, 1, 9, 8, 7, 6, 5, 1, 8, 7, 6, 1, 7, 1, 11, 10, 9, 1, 9, 8, 7, 10, 9, 1, 7, 6, 5, 7, 13, 1, 11, 1, 9, 8, 7, 8, 7, 1, 13, 12, 11, 1, 9, 1, 7, 6, 8, 8, 7, 1, 11, 10, 9, 1, 7, 6, 11, 10, 9, 1, 11

Offset

1,3

Comments

a(n) = 1 iff n+1 is prime.

Links

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

Example

(1!+3!)/(1+3) = 7/4 is not an integer. (2!+3!)/(2+3) = 8/5 is not an integer. (3!+3!)/(3+3) = 12/6 = 2 is an integer. Thus a(3) = 3.

Mathematica

lnk[n_]:=Module[{k=1, nf=n!}, While[!IntegerQ[(k!+nf)/(k+n)], k++]; k]; Array[ lnk, 90] (* Harvey P. Dale, Sep 26 2014 *)

Prog

(PARI) a(n) = for(k=1, oo, if((k!+n!)%(k+n)==0, return(k))); \\ Modified by Jinyuan Wang, Mar 13 2020

Crossrefs

Sequence in context: A166050 A259655 A221185 * A363258 A327642 A358919

Adjacent sequences: A242743 A242744 A242745 * A242747 A242748 A242749

Keyword

nonn

Author

Derek Orr, May 21 2014

Status

approved