%I #39 Jun 04 2024 02:51:39

%S 2,2,5,5,3,2,2,5,5,3,2,11,14,10,8,26,6,17,5,11,5,6,10,15,3,2,19,15,7,

%T 8,5,11,3,14,14,10,6,10,6,11,3,6,18,5,11,5,18,9,5,3,2,3,7,16,17,11,3,

%U 5,9,11,2,6,7,7,11,17,15,8,5,11,5,9,8,5,8,3,2,16,21,11,5,6,14,4,11,22,22,7

%N Least nontrivial exponent e such that n is a substring of n^e.

%H Reinhard Zumkeller and Zak Seidov, <a href="/A045537/b045537.txt">Table of n, a(n) for n = 0..10000</a>. Terms up to a(1000) from Reinhard Zumkeller.

%H Code Golf StackExchange, <a href="https://codegolf.stackexchange.com/questions/176734/self-contained-powers">Self-contained powers</a>, coding challenge started Nov 28 2018.

%H <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>

%F n^a(n) = A104782(n).

%t f[n_] := Block[{k = 2}, While[ StringPosition[ ToString[n^k], ToString[n]] == {}, k++ ]; k]; Table[ f[n], {n, 0, 87}] (* _Robert G. Wilson v_, May 09 2005 *)

%o (Haskell)

%o import Data.List (isInfixOf)

%o a045537 n = 2 + length

%o (takeWhile (not . ((show n) `isInfixOf`) . show) $ iterate (* n) (n^2))

%o -- _Reinhard Zumkeller_, Sep 29 2011

%o (PARI) a(n) = my(s = Str(n), k=2); while (#strsplit(Str(n^k), s) == 1, k++); k; \\ _Michel Marcus_, Jun 04 2024

%Y Cf. A051248, A070327, A104782.

%K base,nonn

%O 0,1

%A _Erich Friedman_