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

1,3

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A009995.

Sequence in context: A032881 A239216 A032848 * A190218 A055569 A351119

Adjacent sequences: A009990 A009991 A009992 * A009994 A009995 A009996

Keyword

nonn,fini,full,base

Author

N. J. A. Sloane

Status

approved