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

1,1

Links

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

Example

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

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

Prog

(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

Crossrefs

Cf. A071176, A245631, A243093.

Sequence in context: A021609 A364966 A140684 * A356983 A158038 A259281

Adjacent sequences: A245629 A245630 A245631 * A245633 A245634 A245635

Keyword

nonn,base

Author

Derek Orr, Jul 27 2014

Status

approved