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A239121 Smallest number k > 0 such that the decimal expansion of k^k contains n. 1

%I

%S 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,

%T 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,

%U 11,7,14,4,18,14,13,19,11,25,17,17,6,6,8,14,27,11,26,8

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

%H Giovanni Resta, <a href="/A239121/b239121.txt">Table of n, a(n) for n = 0..10000</a>

%e a(0) = 9 because 9^9 = 387420489 has "0" as a substring;

%e a(1) = 1 because 1^1 = 1 has "1" as a substring;

%e a(2) = 3 because 3^3 = 27 has "2" as a substring;

%e a(3) = 5 because 5^5 = 3125 has "3" as a substring;

%e a(4) = 2 because 2^2 = 4 has "4" as a substring.

%t 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 *)

%t 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 *)

%o (PARI) overlap(long, short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short, return(1)); long\=10); 0

%o a(n)=my(k); while(!overlap(k++^k, n), ); k \\ _Charles R Greathouse IV_, Mar 11 2014

%Y Cf. A030001.

%K nonn,base

%O 0,1

%A _Michel Lagneau_, Mar 10 2014

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Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)