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%I #41 Aug 05 2023 22:18:20
%S 0,1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24,25,26,27,28,29,34,
%T 35,36,37,38,39,45,46,47,48,49,56,57,58,59,67,68,69,78,79,89,123,124,
%U 125,126,127,128,129,134,135,136,137,138,139,145,146,147,148,149,156,157
%N Numbers whose decimal digits are in strictly increasing order.
%C Sequence has 512 terms, since every term except 0 corresponds to a nonempty subset of {1,2,3,4,5,6,7,8,9}.
%C A178788(a(n)) = 1. - _Reinhard Zumkeller_, Jun 30 2010
%C Number of terms in [10^(n-1), 10^n): 0, 9, 36, 84, 126, 126, 84, 36, 9, 1. - _Robert G. Wilson v_, Jul 20 2014
%H Zak Seidov, <a href="/A009993/b009993.txt">Table of n, a(n) for n = 1..512</a> (full sequence)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Digit.html">Digit</a>
%t Flatten@Table[FromDigits/@Subsets[Range[1, 9], {n}], {n, 0, 9}] (* _Zak Seidov_, May 19 2006 *)
%o (PARI) is_A009993(n)=Set(n=digits(n))==n \\ _M. F. Hasler_, Dec 11 2019
%o (PARI) forsubset(9,s,print1(fromdigits(Vec(s))",")) \\ _M. F. Hasler_, Dec 11 2019
%o (Python)
%o from itertools import combinations
%o def afull(): return [0] + sorted(int("".join(c)) for d in range(1, 10) for c in combinations("123456789", d))
%o print(afull()) # _Michael S. Branicky_, Sep 16 2022
%Y Cf. A009995.
%K nonn,fini,full,base
%O 1,3
%A _N. J. A. Sloane_
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