A245096 Numbers whose squares become cubes if one of their digits is deleted.

4, 9, 10, 20, 30, 35, 46, 54, 96, 100, 200, 300, 325, 395, 411, 520, 800, 1000, 1470, 2000, 2448, 2700, 3000, 3144, 4000, 4209, 4633, 6400, 6947, 9000, 9051, 10000, 12500, 13719, 20000, 21600, 25300, 30000, 34300, 35000, 46000, 51200, 54000, 61632, 72900, 96000

Offset

1,1

Comments

A249853 gives the numbers whose cubes become squares if one of their digits is deleted.

Numbers with single-digit squares are not included. - Davin Park, Dec 30 2016

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

4^2 = 16 and (1)^1/3 = 1.
9^2 = 81 and (8)^1/3 = 2 or (1)^1/3 = 1.
10^2 = 100 and (00)^1/3 = 0.
3144^2 = 9884736 and (884736)^1/3 = 96.

Maple

with(numtheory): P:=proc(q, h) local a, b, k, n;
for n from 4 to q do a:=n^2; for k from 0 to ilog10(a) do
b:=trunc(a/10^(k+1))*10^k+(a mod 10^k);
if b=trunc(evalf((b)^(1/h)))^h then print(n);
break; fi; od; od; end: P(10^9, 3);

Mathematica

f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^2], #] & /@ Range[IntegerLength[n^2]], IntegerQ@CubeRoot@FromDigits@# &];
Select[Range[4, 1000], f] (* Davin Park, Dec 30 2016 *)
scddQ[x_]:=AnyTrue[Table[FromDigits[Delete[IntegerDigits[x^2], n]], {n, IntegerLength[ x^2]}], IntegerQ[CubeRoot[#]]&]; Select[Range[100000], scddQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 02 2018 *)

Crossrefs

Cf. A249853.

Sequence in context: A004631 A316113 A336256 * A352097 A354853 A119718

Adjacent sequences: A245093 A245094 A245095 * A245097 A245098 A245099

Keyword

nonn,base

Author

Paolo P. Lava, Nov 12 2014

Status

approved