A249853 Numbers whose cubes become squares if one of their digits is deleted.

4, 5, 6, 10, 20, 21, 25, 40, 44, 64, 90, 100, 129, 160, 200, 250, 360, 400, 490, 500, 600, 640, 810, 1000, 1210, 1440, 1690, 1960, 2000, 2025, 2100, 2250, 2500, 2560, 2890, 3240, 3610, 4000, 4400, 4410, 4840, 5025, 5290, 5760, 6250, 6400, 6760, 7290, 7840, 8410

Offset: 1

Author

Paolo P. Lava, Nov 07 2014

Keywords

• nonn
• base

Comments

A245096 gives the numbers whose squares become cubes if one of their digit is deleted.

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

Examples

			21^3 = 9261 and sqrt(961) = 31.
44^3 = 85184 and sqrt(5184) = 72.
45625^3 = 94974853515625 and sqrt(9474853515625) = 3078125.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 100 terms from Paolo P. Lava)

Crossrefs

Cf. A249587, A225885.

Programs

Maple

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

Mathematica

f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^3], #] & /@ Range[IntegerLength[n^3]], IntegerQ@Sqrt@FromDigits@# &];
Select[Range[4, 1000], f] (* Davin Park, Dec 30 2016 *)