A134846 Smallest number k containing no zero digit such that k^2 contains exactly n zeros.

32, 245, 448, 3747, 24495, 62498, 248998, 2449552, 6393747, 6244998, 244949995, 498998998, 2449489753, 24498999998, 28284271249, 248997999998, 498998999999, 4989989999997, 24899979999998

Offset: 1

Author

Artur Jasinski, Nov 13 2007

Keywords

• nonn
• base
• more

Comments

The corresponding squares are in A134847.

Browkin (see link, p. 29) gives a number without zero digits whose square has 26 zeros: 4472135954999579392819^2 = 20000000000000000000005837591200400708766761. However, he does not claim that it is the smallest such number, so a(26) <= 4472135954999579392819.

Indeed, there are much smaller candidates for a(26), such as 489899998999999999. We also have a(20) <= 49899989999999 and a(21) <= 498998998999998. - Giovanni Resta, Jun 28 2019

Examples

			a(1) = 32 because 32 is the smallest number without zero digits whose square has exactly one zero: 1024.
		

Links

• Jerzy Browkin, Groebner basis (in Polish)

Crossrefs

Cf. A134843, A134844, A134845, A134847.

Extensions

Edited and a(11), a(12), a(13) added by Klaus Brockhaus, Nov 20 2007

a(14)-a(15) from Lars Blomberg, Jun 25 2011

a(16)-a(19) from Giovanni Resta, Jun 28 2019