A265261 Smallest n-Knödel number, i.e., smallest composite c > n such that each b < c coprime to c satisfies b^(c-n) == 1 (mod c).

561, 4, 9, 6, 25, 8, 15, 12, 21, 12, 15, 16, 33, 24, 21, 20, 65, 24, 51, 24, 45, 24, 33, 32, 69, 30, 39, 40, 65, 36, 87, 40, 45, 44, 51, 40, 85, 56, 57, 48, 65, 72, 91, 48, 63, 66, 69, 60, 141, 56, 63, 60, 65, 72, 75, 60, 63, 70, 87, 72, 133, 122, 93, 80, 165

Offset: 1

Author

Felix Fröhlich, Apr 06 2016

Keywords

• nonn

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..4000
• Wikipedia, Knödel number.

Crossrefs

Cf. A050990, A033553, A050992, A050993, A208154, A208155, A208156, A208157, A208158.

Programs

Mathematica

Table[SelectFirst[Range[n + 1, 10^3], Function[c, CompositeQ@ c && AllTrue[Range[1, c - 1] /. x_ /; ! CoprimeQ[x, c] -> Nothing, Mod[#^(c - n), c] == 1 &]]], {n, 65}] (* Michael De Vlieger, Apr 06 2016, Version 10 *)

PARI

a(n) = forcomposite(c=n+1, , my(i=0, j=0); for(b=1, c-1, if(gcd(b, c)==1, i++; if(Mod(b, c)^(c-n)==1, j++))); if(i==j, return(c)))