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A245632 Least number k such that n concatenated with k is a perfect power.

%I A245632 #17 Jun 05 2021 12:32:32
%S A245632 6,5,2,9,12,4,29,1,61,0,56,1,31,4,21,9,28,49,6,25,6,5,104,3,6,244,44,
%T A245632 9,16,25,25,4,64,3,344,1,21,44,69,0,209,25,56,1,369,24,61,4,13,41,2,9,
%U A245632 29,76,225,25,6,32,29,84,504,5,504,516,61,564,6,59,169,56,289,9,96,529,69,176,44,4,21,656
%N A245632 Least number k such that n concatenated with k is a perfect power.
%H A245632 Jens Kruse Andersen, <a href="/A245632/b245632.txt">Table of n, a(n) for n = 1..10000</a>
%e A245632 16 is the smallest perfect power > 9 beginning with 1. Thus a(1) = 6.
%p A245632 conc:= proc(n,k) if k = 0 then 10*n else 10^(1+ilog10(k))*n+k fi end proc:
%p A245632 ispow:= proc(x) local F; F:= ifactors(x)[2];
%p A245632 evalb(igcd(seq(f[2],f=F))>1) end proc:
%p A245632 a:= proc(n) local k; for k from 0 do if ispow(conc(n,k)) then return k fi od end proc;
%p A245632 seq(a(n),n=1..100); # _Robert Israel_, Jul 28 2014
%o A245632 (PARI)
%o A245632 a(n)=p="";for(k=0,oo,p=concat(Str(n),Str(k));if(ispower(eval(p)),return(k)))
%o A245632 n=1;while(n<100,print1(a(n),", ");n++)
%o A245632 (Python)
%o A245632 from sympy import perfect_power
%o A245632 def a(n):
%o A245632     s, k = str(n), 0
%o A245632     while not perfect_power(int(s+str(k))): k += 1
%o A245632     return k
%o A245632 print([a(n) for n in range(1, 81)]) # _Michael S. Branicky_, Jun 05 2021
%Y A245632 Cf. A071176, A245631, A243093.
%K A245632 nonn,base
%O A245632 1,1
%A A245632 _Derek Orr_, Jul 27 2014