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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 (list; graph; refs; listen; history; text; internal format)
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^(10n-1) (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*n-1)*log(10)/log(k)), 10*n*log(10)/log(k), v=vecsort(digits(k^e)); for(i=1, 9, if(v[i*n]!=i-1 || 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

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Last modified January 19 00:03 EST 2021. Contains 340262 sequences. (Running on oeis4.)