A271669 Smallest k > n such that n divides k and n^k == n (mod k).

2, 161038, 6, 12, 10, 30, 14, 56, 18, 30, 22, 132, 26, 182, 30, 48, 34, 306, 38, 380, 42, 66, 46, 552, 50, 130, 54, 84, 58, 870, 62, 992, 66, 102, 70, 180, 74, 1406, 78, 120, 82, 1722, 86, 1892, 90, 138, 94, 2256, 98, 350, 102, 156, 106, 2862, 110, 280, 114, 174, 118, 3540

Offset: 1

Author

Thomas Ordowski, Apr 12 2016

Keywords

• nonn

Examples

			Because of the definition of (pseudo)primes to base 2, a(2) is the least element of A006935 greater than 2. - _Altug Alkan_, Apr 12 2016
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006935, A102457.

Programs

Mathematica

Table[SelectFirst[Range[n + 1, 10^6], Function[k, Divisible[k, n] && PowerMod[n, k, k] == Mod[n, k]]], {n, 60}] (* Michael De Vlieger, Apr 12 2016, Version 10 *)
skn[n_]:=Module[{k=2n},While[PowerMod[n,k,k]!=n,k=k+n];k]; Array[skn,60] (* Harvey P. Dale, Jan 20 2025 *)

PARI

a(n) = {k = n+1; while( !(((k % n)==0) && (Mod(n,k)^k == Mod(n, k))), k++); k;} \\ Michel Marcus, Apr 12 2016

Formula

a(n) = 2n for odd n. - Robert Israel, Apr 12 2016

a(n) = n * A102457(n) for n > 1. - Thomas Ordowski, Apr 13 2016

Extensions

More terms from Michel Marcus, Apr 12 2016