A253600 Smallest exponent k>1 such that n and n^k have some digits in common.

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

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

Mathematica

seq={}; Do[k=1; Until[ContainsAny[IntegerDigits[n], IntegerDigits[n^k]], k++]; AppendTo[seq, k] , {n, 0, 86}]; seq (* James C. McMahon, Jun 04 2024 *)

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).

Cf. A373203.

Sequence in context: A283825 A005177 A357123 * A373203 A045537 A243941

Adjacent sequences: A253597 A253598 A253599 * A253601 A253602 A253603

Keyword

nonn,base

Author

Michel Marcus, Jan 05 2015

Status

approved