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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A249587, A225885.

Sequence in context: A001609 A101590 A057916 * A162415 A007606 A284513

Adjacent sequences: A249850 A249851 A249852 * A249854 A249855 A249856

Keyword

nonn,base

Author

Paolo P. Lava, Nov 07 2014

Status

approved