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
Examples
For n=2, 2^k has no digit in common with 2 until k reaches 5 to give 32, hence a(2)=5.
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Crossrefs
Programs
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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 *) -
PARI
a(n) = {sd = Set(vecsort(digits(n))); k=2; while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); k;}
Comments