A161750 Numbers n such that the decimal digits of 123456789*n are all distinct.

0, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 20, 22, 23, 25, 26, 31, 32, 34, 35, 40, 41, 43, 44, 50, 52, 53, 61, 62, 70, 71, 80

Offset: 1

Author

Kyle Stern, Jun 17 2009

Keywords

• easy
• fini
• full
• nonn
• base

Links

• David Wolfe, When Multiplication Mixes Up Digits, Mathematics Magazine, Volume 80, Number 5, December 2007, pp.380-383

Crossrefs

Cf. A053654. [From Zak Seidov, Nov 04 2009]

Programs

Maple

a := proc (n) local nn, nnn: nn := convert(123456789*n, base, 10): nnn := convert(nn, set): if nops(nn) = nops(nnn) then n else end if end proc: seq(a(n), n = 1 .. 80); # Emeric Deutsch, Jun 21 2009

Mathematica

m=123456789;se=Select[Range[0,99],Sort[id=IntegerDigits[m*# ]]==Union[id]&] (* Zak Seidov, Nov 04 2009 *)
Select[Range[0,100],Max[DigitCount[123456789#]]==1&] (* Harvey P. Dale, Jun 02 2017 *)

Extensions

a(1)=0 added by Zak Seidov, Nov 04 2009

Edited by Charles R Greathouse IV, Aug 02 2010