A161750 - OEIS

%I #13 Jun 02 2017 10:33:42

%S 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,

%T 44,50,52,53,61,62,70,71,80

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

%H David Wolfe, <a href="http://homepages.gac.edu/~wolfe/papers/pandigital/mathmag.pdf">When Multiplication Mixes Up Digits</a>, Mathematics Magazine, Volume 80, Number 5, December 2007, pp.380-383

%p 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

%t m=123456789;se=Select[Range[0,99],Sort[id=IntegerDigits[m*# ]]==Union[id]&] (* _Zak Seidov_, Nov 04 2009 *)

%t Select[Range[0,100],Max[DigitCount[123456789#]]==1&] (* _Harvey P. Dale_, Jun 02 2017 *)

%Y Cf. A053654. [From _Zak Seidov_, Nov 04 2009]

%K easy,fini,full,nonn,base

%O 1,3

%A _Kyle Stern_, Jun 17 2009

%E a(1)=0 added by _Zak Seidov_, Nov 04 2009

%E Edited by _Charles R Greathouse IV_, Aug 02 2010