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

%I A243092 #23 Feb 21 2023 02:17:37
%S A243092 25,7,43,913,12,859,29,5184,261,648,7649,167,31,8877,625,6375,28,5193,
%T A243092 683,5379,97,6981,8328,389,15456,2144,44,7496,791,48625,4432,768,75,
%U A243092 3000,937,52264,3248,9017,304,96,73281,875,8976,10944,6533,656,4552,26809,3039,653,2000,68024
%N A243092 Least number k > n such that n concatenated with k produces a cube.
%C A243092 Differs from A245631 at n = 6, 12, 21, 34, 49, 51, 58, 68, 72, 92, ... - _Chai Wah Wu_, Feb 20 2023
%H A243092 Chai Wah Wu, <a href="/A243092/b243092.txt">Table of n, a(n) for n = 1..10000</a>
%e A243092 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.
%t A243092 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 *)
%o A243092 (PARI)
%o A243092 a(n)=s=Str(n);k=n+1; while(!(ispower(eval(concat(s, Str(k))), 3)), k++); return(k)
%o A243092 vector(100, n, a(n))
%o A243092 (Python)
%o A243092 from sympy import integer_nthroot
%o A243092 def A243092(n):
%o A243092     m, a = 10*n, 10**(len(str(n))-1)
%o A243092     while (k:=(integer_nthroot(a*(m+1)-1,3)[0]+1)**3-m*a)>=10*a or k<=n:
%o A243092         a *= 10
%o A243092     return k # _Chai Wah Wu_, Feb 20 2023
%Y A243092 Cf. A245631.
%K A243092 nonn,base
%O A243092 1,1
%A A243092 _Derek Orr_, Aug 18 2014
%E A243092 Improvement to PARI code by _Colin Barker_, Aug 18 2014