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

Author

Paolo P. Lava, Nov 12 2014

Keywords

• nonn
• base

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A249853.

Programs

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 *)