

A217368


Smallest number having a power that in decimal has exactly n copies of all ten digits.


3



32043, 69636, 643905, 421359, 320127, 3976581, 47745831, 15763347, 31064268, 44626422, 248967789, 85810806, 458764971, 500282265, 2068553967, 711974055, 2652652791, 901992825, 175536645, 3048377607, 3322858521, 1427472867, 3730866429, 9793730157
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OFFSET

1,1


COMMENTS

The exponents that produce the number with a fixed number of copies of each digit are listed in sequence A217378. See there for further comments.
Since we allow A217378(n)=1, the sequence is well defined, with the upper bound a(n) <= 100...99 ~ 10^(10n1) (n copies of each digit, sorted in increasing order, except for one "1" permuted to the first position).  M. F. Hasler, Oct 05 2012
What is the minimum value of a(n)? Can it be proved that a(n) > 2 for all n?  Charles R Greathouse IV, Oct 16 2012


LINKS

Table of n, a(n) for n=1..24.


EXAMPLE

The third term raised to the fifth power (A217378(3)=5), 643905^5 = 110690152879433875483274690625, has three copies of each digit (in its decimal representation), and no number smaller than 643905 has a power with this feature.


MATHEMATICA

f[n_] := Block[{k = 2, t = Table[n, {10}], r = Range[0, 9]}, While[c = Count[ IntegerDigits[k^Floor[ Log[k, 10^(10 n)]]], #] & /@ r; c != t, k++]; k] (* Robert G. Wilson v, Nov 28 2012 *)


PROG

(PARI) is(n, k)=my(v); for(e=ceil((10*n1)*log(10)/log(k)), 10*n*log(10)/log(k), v=vecsort(digits(k^e)); for(i=1, 9, if(v[i*n]!=i1  v[i*n+1]!=i, return(0))); return(1)); 0
a(n)=my(k=2); while(!is(n, k), k++); k \\ Charles R Greathouse IV, Oct 16 2012


CROSSREFS

Cf. A020666, A054038, A054039, A066825, A067635, A074205, A156977, A217378.
Sequence in context: A231613 A054038 A156977 * A097282 A264499 A249230
Adjacent sequences: A217365 A217366 A217367 * A217369 A217370 A217371


KEYWORD

nonn,base


AUTHOR

James G. Merickel, Oct 01 2012


EXTENSIONS

a(13)a(14) from James G. Merickel, Oct 06 2012 and Oct 08 2012
a(15)a(16) from Charles R Greathouse IV, Oct 17 2012
a(17)a(19) from Charles R Greathouse IV, Oct 18 2012
a(20) from Charles R Greathouse IV, Oct 22 2012
a(21)a(24) from Giovanni Resta, May 05 2017


STATUS

approved



