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A253600 Smallest exponent k>1 such that n and n^k have some digits in common. 3
2, 2, 5, 5, 3, 2, 2, 5, 5, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 5, 3, 2, 2, 3, 3, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 3, 2, 2, 2, 2, 3, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For all n, n^5-n is divisible by 10, and so n^5 == n (mod 10). Thus a(n) <= 5 for all n. - Tom Edgar, Jan 06 2015

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

EXAMPLE

For n=2, 2^k has no digit in common with 2 until k reaches 5 to give 32, hence a(2)=5.

MAPLE

f:= proc(n) local L, k;

L:= convert(convert(n, base, 10), set);

for k from 2 do

   if convert(convert(n^k, base, 10), set) intersect L <> {} then

     return k

   fi

od

end proc:

map(f, [$0..100]); # Robert Israel, Mar 17 2020

PROG

(PARI) a(n) = {sd = Set(vecsort(digits(n))); k=2; while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); k; }

CROSSREFS

Cf. sequences where a(n)=k: A103173 (k=5), A189056 (k=2), A253601 (k=3), A253602 (k=4).

Sequence in context: A210713 A283825 A005177 * A045537 A243941 A161622

Adjacent sequences:  A253597 A253598 A253599 * A253601 A253602 A253603

KEYWORD

nonn,base

AUTHOR

Michel Marcus, Jan 05 2015

STATUS

approved

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Last modified August 9 18:55 EDT 2022. Contains 356026 sequences. (Running on oeis4.)