A126762 a(n) is the least k > n such that the remainder when n^k is divided by k is n.

2, 3, 5, 5, 7, 7, 11, 9, 11, 11, 13, 13, 17, 15, 17, 17, 19, 19, 23, 21, 23, 23, 29, 25, 28, 27, 29, 29, 31, 31, 37, 33, 37, 35, 37, 37, 41, 39, 41, 41, 43, 43, 47, 45, 47, 47, 53, 49, 53, 51, 53, 53, 59, 55, 59, 57, 59, 59, 61, 61, 67, 63, 67, 65, 67, 67, 71, 69, 71, 71, 73, 73

Offset: 1

Author

Alexander Adamchuk, Feb 17 2007

Keywords

• nonn

Comments

a(n-1) = n for n = {2,3,5,7,9,11,13,15,17,19,21,23,25,27,29,...} = 2 together with odd numbers n > 1.

a(n) coincides with A082048(n) up to n = 24.

a(n) is the smallest number k > n such that n^k == n (mod k). Conjecture: a(n) is the smallest number k > n such that n^(k-1) == 1 (mod k). Thus a(n) is coprime to n. - Thomas Ordowski, Aug 03 2018

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..996

Crossrefs

Cf. A128149 = Least k such that n^k (mod k) = n-1. Cf. A128172 = Least k such that n^k (mod k) = n+1. Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159, A128160. Cf. A082048 = least number greater than n having greater smallest prime factor than that of n.

Programs

Mathematica

Table[Min[Select[Range[101],PowerMod[n,#,# ]==n&]],{n,1,100}]
lkgn[n_]:=Module[{k=1},While[PowerMod[n,k,k]!=n,k++];k]; Array[lkgn,80] (* Harvey P. Dale, May 25 2021 *)

Extensions

Name clarified by Thomas Ordowski, Aug 03 2018