

A239121


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


1



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
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OFFSET

0,1


LINKS

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


EXAMPLE

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.


MATHEMATICA

a[n_] := (k = 1; While[ !MatchQ[ IntegerDigits[k^k], {___, Sequence @@ IntegerDigits[n], ___}], k++]; k); Table[a[n], {n, 0, 80}] (*program from JeanFrancois 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 *)


PROG

(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


CROSSREFS

Cf. A030001.
Sequence in context: A198835 A010167 A154181 * A019875 A248557 A198819
Adjacent sequences: A239118 A239119 A239120 * A239122 A239123 A239124


KEYWORD

nonn,base


AUTHOR

Michel Lagneau, Mar 10 2014


STATUS

approved



