cp's OEIS Frontend

A248127 Numbers whose squares became cubes if some digit is prepended, inserted or appended.

%I A248127 #31 Dec 31 2016 07:24:24
%S A248127 2,4,5,10,31,72,75,80,162,270,383,640,1250,2000,2160,3430,4000,5000,
%T A248127 5120,7290,10000,13310,17280,21970,27440,28875,31000,33750,40960,
%U A248127 49130,58320,68590,72000,75000,80000,92610
%N A248127 Numbers whose squares became cubes if some digit is prepended, inserted or appended.
%e A248127 If n = 10 then n^2 = 100 and if we append a 0 we have (1000)^1/3 = 10.
%e A248127 If n = 31 then n^2 = 961 and if we insert a 2 we have (9261)^1/3 = 21.
%e A248127 Again, if n = 112625 then n^2 = 12684390625 and if we insert an 8 we have (126884390625)^1/3 = 5025.
%p A248127 with(numtheory): P:=proc(q) local a, b, c, j, k, ok, n;
%p A248127 for n from 1 to q do a:=n^2; c:=ilog10(a)+1; ok:=1; for k from 0 to ilog10(a)+1 do
%p A248127 if ok=1 then for j from 0 to 9 do if not (k=c and j=0) then b:=trunc(a/10^k)*10^(k+1)+j*10^k+(a mod 10^k);
%p A248127 if b=trunc(evalf((b)^(1/3)))^3 then print(n); ok:=0; break; fi; fi; od; fi; od; od; end: P(10^9);
%t A248127 f[n_] := ! MissingQ@SelectFirst[Rest@Flatten[Outer[Insert[IntegerDigits[n^2], #2, #1] &, Range[IntegerLength[n^2] + 1], Range[0, 9]], 1], IntegerQ@CubeRoot@FromDigits@# &];
%t A248127 Select[Range[100], f] (* _Davin Park_, Dec 30 2016 *)
%Y A248127 Cf. A248051, A249853.
%K A248127 nonn,base
%O A248127 1,1
%A A248127 _Paolo P. Lava_, Nov 10 2014
%E A248127 Corrected by _Davin Park_, Dec 30 2016