A328783 Numbers k such that k and k^2 contain at least one zero but not the same number of 0's.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 202, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 301, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 401, 410, 420, 430, 440, 450, 460, 470

Offset: 1

Author

Bernard Schott, Oct 28 2019

Keywords

• nonn
• base

Comments

This sequence is one of the three sequences whose numbers k and k^2 don't contain the same number of 0, the two others are A104315 and A134844.

Examples

			201 and 40401 = 201^2 have both at least one zero but not the same number of 0 in their decimal expansion, hence, 201 is a term.
		

Links

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

Crossrefs

Cf. A052040, A104315, A134844, A328780, A328781, A328782.

Programs

Maple

f:= n-> numboccur(0, convert(n, base, 10)):
q:= n-> ((x, y)-> x>0 and y>0 and x<>y)(f(n), f(n^2)):
select(q, [$0..500])[];  # Alois P. Heinz, Oct 28 2019

Mathematica

Select[Range[0, 470], (x = DigitCount[#, 10, 0]) > 0 && (y = DigitCount[ #^2, 10, 0]) > 0 && x != y &] (* Giovanni Resta, Feb 27 2020 *)

Extensions

More terms from Alois P. Heinz, Oct 28 2019