A245631 Least number k such that n concatenated with k produces a cube.

25, 7, 43, 913, 12, 4, 29, 5184, 261, 648, 7649, 5, 31, 8877, 625, 6375, 28, 5193, 683, 5379, 6, 6981, 8328, 389, 15456, 2144, 44, 7496, 791, 48625, 4432, 768, 75, 3, 937, 52264, 3248, 9017, 304, 96, 73281, 875, 8976, 10944, 6533, 656, 4552, 26809, 13, 653, 2, 68024, 1441, 872, 1368, 39752, 1787, 32, 319

Offset: 1

Author

Derek Orr, Jul 27 2014

Keywords

• nonn
• base

Examples

			20, 21, 22, 23, 24, 25, and 26 are not cubes. 27 is a cube. Thus a(2) = 7.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Jens Kruse Andersen)

Crossrefs

Cf. A071176.

Programs

Mathematica

lnc[n_]:=Module[{k=1},While[!IntegerQ[Surd[n*10^IntegerLength[k]+k,3]],k++];k]; Array[lnc,60] (* Harvey P. Dale, Aug 08 2019 *)

PARI

a(n)=p="";for(k=0,10^6,p=concat(Str(n),Str(k));if(ispower(eval(p))&&ispower(eval(p))%3==0,return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

Python

from sympy import integer_nthroot
def A245631(n):
    m = 10*n
    if integer_nthroot(m,3)[1]: return 0
    a = 1
    while (k:=(integer_nthroot(a*(m+1)-1,3)[0]+1)**3-m*a)>=10*a:
        a *= 10
    return k # Chai Wah Wu, Feb 15 2023