A239121 Smallest number k > 0 such that the decimal expansion of k^k contains n.

9, 1, 3, 5, 2, 4, 4, 3, 7, 9, 10, 11, 5, 19, 22, 26, 8, 17, 16, 19, 9, 8, 13, 7, 17, 4, 17, 3, 11, 18, 13, 5, 23, 17, 18, 7, 17, 15, 9, 18, 16, 17, 9, 7, 12, 28, 6, 23, 9, 24, 23, 13, 18, 11, 7, 14, 4, 18, 14, 13, 19, 11, 25, 17, 17, 6, 6, 8, 14, 27, 11, 26, 8

Offset: 0

Author

Michel Lagneau, Mar 10 2014

Keywords

• nonn
• base

Examples

			a(0) = 9 because 9^9 = 387420489 has "0" as a substring;
a(1) = 1 because 1^1 = 1 has "1" as a substring;
a(2) = 3 because 3^3 = 27 has "2" as a substring;
a(3) = 5 because 5^5 = 3125 has "3" as a substring;
a(4) = 2 because 2^2 = 4 has "4" as a substring.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A030001.

Programs

Mathematica

a[n_] := (k = 1; While[ !MatchQ[ IntegerDigits[k^k], {_, Sequence @@ IntegerDigits[n], _}], k++]; k); Table[a[n], {n, 0, 80}] (*program from Jean-Francois Alcover adapted for this sequence - see A030001 *)
snk[n_]:=Module[{k=1},While[SequenceCount[IntegerDigits[k^k],IntegerDigits[ n]]<1,k++];k]; Array[snk,80,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 09 2019 *)

PARI

overlap(long, short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short, return(1)); long\=10); 0
a(n)=my(k); while(!overlap(k++^k, n), ); k \\ Charles R Greathouse IV, Mar 11 2014