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

2, 4, 5, 10, 31, 72, 75, 80, 162, 270, 383, 640, 1250, 2000, 2160, 3430, 4000, 5000, 5120, 7290, 10000, 13310, 17280, 21970, 27440, 28875, 31000, 33750, 40960, 49130, 58320, 68590, 72000, 75000, 80000, 92610

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

If n = 10 then n^2 = 100 and if we append a 0 we have (1000)^1/3 = 10.
If n = 31 then n^2 = 961 and if we insert a 2 we have (9261)^1/3 = 21.
Again, if n = 112625 then n^2 = 12684390625 and if we insert an 8 we have (126884390625)^1/3 = 5025.

Maple

with(numtheory): P:=proc(q) local a, b, c, j, k, ok, n;
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
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);
if b=trunc(evalf((b)^(1/3)))^3 then print(n); ok:=0; break; fi; fi; od; fi; od; od; end: P(10^9);

Mathematica

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@# &];
Select[Range[100], f] (* Davin Park, Dec 30 2016 *)

Crossrefs

Cf. A248051, A249853.

Sequence in context: A110789 A125952 A337661 * A258253 A177244 A367368

Adjacent sequences: A248124 A248125 A248126 * A248128 A248129 A248130

Keyword

nonn,base

Author

Paolo P. Lava, Nov 10 2014

Extensions

Corrected by Davin Park, Dec 30 2016

Status

approved