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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A245631.

Sequence in context: A040606 A091736 A245631 * A126837 A248583 A080203

Adjacent sequences: A243089 A243090 A243091 * A243093 A243094 A243095

Keyword

nonn,base

Author

Derek Orr, Aug 18 2014

Extensions

Improvement to PARI code by Colin Barker, Aug 18 2014

Status

approved