

A225842


Least k such that some digit occurs n times (or more) in the decimal representation of n^k.


2



0, 0, 16, 11, 23, 25, 28, 33, 31, 45, 10, 46, 61, 60, 66, 62, 66, 73, 76, 76, 20, 76, 91, 116, 109, 105, 122, 125, 105, 121, 29, 130, 115, 132, 132, 164, 153, 159, 162, 152, 39, 178, 182, 163, 181, 174, 186, 195, 180, 204, 45, 179, 221, 217, 224, 225, 245, 215, 208, 252, 55, 215
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OFFSET

0,3


COMMENTS

a(10^j) = ceiling((10^j) / j) for any j > 0.
a(i*10^j) <= ceiling((i*10^j) / j) for any i > 0 and j > 0.


LINKS



EXAMPLE

3^11 = 177147 is the first power of 3 with some digit occurring 3 times in its decimal representation. Hence a(3)=11.


MATHEMATICA

a[n_] := If[n < 2, 0, Block[{k = 1}, While[Max[DigitCount[n^k]] < n, k++]; k]]; Array[a, 62, 0] (* Giovanni Resta, May 17 2013 *)


PROG

(PARI) mddo(n)=my(c=vector(10), m=0, d); while(n>0, d=n%10; n=n\10; c[d+1]=1+c[d+1]; m=max(c[d+1], m)); return(m)
a(n)=my(k=0, p=1); while(mddo(p)<n, k=k+1; p=p*n); return(k)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



