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

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, 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, 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

Offset: 1

Author

Derek Orr, Jul 27 2014

Keywords

• nonn
• base

Examples

			16 is the smallest perfect power > 9 beginning with 1. Thus a(1) = 6.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071176, A245631, A243093.

Programs

Maple

conc:= proc(n,k) if k = 0 then 10*n else 10^(1+ilog10(k))*n+k fi end proc:
ispow:= proc(x) local F; F:= ifactors(x)[2];
evalb(igcd(seq(f[2],f=F))>1) end proc:
a:= proc(n) local k; for k from 0 do if ispow(conc(n,k)) then return k fi od end proc;
seq(a(n),n=1..100); # Robert Israel, Jul 28 2014

PARI

a(n)=p="";for(k=0,oo,p=concat(Str(n),Str(k));if(ispower(eval(p)),return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

Python

from sympy import perfect_power
def a(n):
    s, k = str(n), 0
    while not perfect_power(int(s+str(k))): k += 1
    return k
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Jun 05 2021