A243092 Least number k > n such that n concatenated with k produces a cube.

25, 7, 43, 913, 12, 859, 29, 5184, 261, 648, 7649, 167, 31, 8877, 625, 6375, 28, 5193, 683, 5379, 97, 6981, 8328, 389, 15456, 2144, 44, 7496, 791, 48625, 4432, 768, 75, 3000, 937, 52264, 3248, 9017, 304, 96, 73281, 875, 8976, 10944, 6533, 656, 4552, 26809, 3039, 653, 2000, 68024

Offset: 1

Author

Derek Orr, Aug 18 2014

Keywords

• nonn
• base

Comments

Differs from A245631 at n = 6, 12, 21, 34, 49, 51, 58, 68, 72, 92, ... - Chai Wah Wu, Feb 20 2023

Examples

			23 is not a cube. 24 is not a cube. 25 is not a cube. 26 is not a cube. 27 is a cube. Thus a(2) = 7.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A245631.

Programs

Mathematica

lnk[n_]:=Module[{k=n+1},While[!IntegerQ[Surd[n*10^IntegerLength[k]+k,3]],k++];k]; Array[lnk,60] (* Harvey P. Dale, Oct 14 2021 *)

PARI

a(n)=s=Str(n);k=n+1; while(!(ispower(eval(concat(s, Str(k))), 3)), k++); return(k)
vector(100, n, a(n))

Python

from sympy import integer_nthroot
def A243092(n):
    m, a = 10*n, 10**(len(str(n))-1)
    while (k:=(integer_nthroot(a*(m+1)-1,3)[0]+1)**3-m*a)>=10*a or k<=n:
        a *= 10
    return k # Chai Wah Wu, Feb 20 2023

Extensions

Improvement to PARI code by Colin Barker, Aug 18 2014