A328782 Integers k such that k and k^2 contain the same number > 0 of digits zero in their decimal expansion.

0, 104, 105, 203, 205, 302, 303, 305, 402, 403, 405, 504, 505, 506, 507, 508, 509, 601, 602, 603, 605, 609, 701, 702, 703, 705, 708, 709, 801, 802, 803, 805, 901, 902, 903, 905, 906, 1006, 1007, 1008, 1009, 1011, 1012, 1013, 1014, 1016, 1017, 1018, 1019, 1021

Offset: 1

Author

Bernard Schott, Oct 28 2019

Keywords

• nonn
• base

Examples

			703 and 494209 = 703^2 both have one zero digit in their decimal expansion.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Equals A328781 \ A052040.

Cf. A104315, A134844, A328780, A328783.

Programs

Maple

f:= n-> numboccur(0, convert(n, base, 10)):
q:= n-> ((x, y)-> x>0 and x=y)(f(n), f(n^2)):
select(q, [$0..1030])[];  # Alois P. Heinz, Oct 28 2019

Mathematica

Select[Range[0, 1100], DigitCount[#, 10, 0] == DigitCount[#^2, 10, 0] > 0 &] (* Giovanni Resta, Feb 27 2020 *)

Extensions

More terms from Alois P. Heinz, Oct 28 2019