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Numbers with exactly three distinct base-10 digits.
6

%I #26 Aug 10 2021 18:46:27

%S 102,103,104,105,106,107,108,109,120,123,124,125,126,127,128,129,130,

%T 132,134,135,136,137,138,139,140,142,143,145,146,147,148,149,150,152,

%U 153,154,156,157,158,159,160,162,163,164,165,167,168,169,170,172,173,174

%N Numbers with exactly three distinct base-10 digits.

%H Robert Israel, <a href="/A031962/b031962.txt">Table of n, a(n) for n = 1..10000</a> (first 648 terms from T. D. Noe)

%p f:= proc(d,b) uses combinat; local S,Res,A1,A1p,A2,x1,x2;

%p Res:= NULL:

%p for S in choose({$0..b-1},3) do

%p x1:= S[3]*(b^d-1)/(b-1);

%p for A1 in powerset(d) minus {{}} do

%p if S[1]=0 and member(d,A1) then next fi;

%p x2:= x1 + (S[1]-S[3])*add(b^(j-1),j=A1);

%p A1p:= {$1..d} minus A1;

%p for A2 in powerset(A1p) minus {{},A1p} do

%p Res:= Res, x2 + (S[2]-S[3])*add(b^(j-1),j=A2);

%p od

%p od

%p od;

%p op(sort([Res]));

%p end proc:

%p f(3,10),f(4,10); # _Robert Israel_, Oct 29 2018

%t Select[Range[100, 200], Length[Union[IntegerDigits[#]]] == 3 &] (* _T. D. Noe_, Dec 04 2012 *)

%t Select[Range[100,200],Count[DigitCount[#],0]==7&] (* _Harvey P. Dale_, May 22 2020 *)

%o (PARI) isok(n) = #Set(digits(n)) == 3; \\ _Michel Marcus_, Oct 29 2018

%Y Cf. A031956, A031957, A031958, A031959, A031960, A031961.

%K nonn,base

%O 1,1

%A _Clark Kimberling_

%E Edited by _Robert Israel_, Oct 29 2018