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A248127 Numbers whose squares became cubes if some digit is prepended, inserted or appended. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A239819 A110789 A125952 * A258253 A177244 A296346

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

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Last modified July 5 01:46 EDT 2020. Contains 335457 sequences. (Running on oeis4.)