A009993 Numbers whose decimal digits are in strictly increasing order.

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, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 156, 157

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full
• base

Comments

Sequence has 512 terms, since every term except 0 corresponds to a nonempty subset of {1,2,3,4,5,6,7,8,9}.

A178788(a(n)) = 1. - Reinhard Zumkeller, Jun 30 2010

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

Links

• Zak Seidov, Table of n, a(n) for n = 1..512 (full sequence)
• Eric Weisstein's World of Mathematics, Digit

Crossrefs

Cf. A009995.

Programs

Mathematica

Flatten@Table[FromDigits/@Subsets[Range[1, 9], {n}], {n, 0, 9}] (* Zak Seidov, May 19 2006 *)

PARI

is_A009993(n)=Set(n=digits(n))==n \\ M. F. Hasler, Dec 11 2019

PARI

forsubset(9,s,print1(fromdigits(Vec(s))",")) \\ M. F. Hasler, Dec 11 2019

Python

from itertools import combinations
def afull(): return [0] + sorted(int("".join(c)) for d in range(1, 10) for c in combinations("123456789", d))
print(afull()) # Michael S. Branicky, Sep 16 2022