A358097 -id:A358097 - cp's OEIS frontend

A030283 a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 30, 41, 50, 61, 70, 81, 90, 111, 200, 311, 400, 511, 600, 711, 800, 911, 2000, 3111, 4000, 5111, 6000, 7111, 8000, 9111, 20000, 31111, 40000, 51111, 60000, 71111, 80000, 91111, 200000, 311111, 400000, 511111, 600000

Offset: 0

Patrick De Geest

The sequence is infinite.

Reinhard Zumkeller, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,0,10,0,-10).

Cf. A358097.

Cf. A068860, A068861, A229363, A229364.

a030283 n = a030283_list !! n
a030283_list = 0 : f 1 9 0 where
   f u v w = w' : f u' v' w' where
     w' = until (> w) ((+ v) . (* 10)) u
     (u',v') = h u v
     h 1 0 = (2,2); h 9 0 = (1,1); h 9 1 = (2,0); h 9 9 = (1,0)
     h u 2 = (u+1,0); h u v = (u+1,1-v)
-- Reinhard Zumkeller, May 03 2012

a = {0}; For[n = 1, n < 1000000, n++, If[Length[Intersection[IntegerDigits[n], IntegerDigits[a[[ -1]]]]] == 0, AppendTo[a, n]]]; a (* Stefan Steinerberger, May 30 2007 *)

a(n) = a(n-2) + 10*a(n-8) - 10*a(n-10) for n > 29. - Nicolas Bělohoubek, Jul 01 2024

Edited by N. J. A. Sloane at the suggestion of Rick L. Shepherd, Sep 27 2007

Definition clarified by Harvey P. Dale, Oct 19 2012

A358098 a(n) is the largest integer m < n such that m and n have no common digit, or -1 when such integer m does not exist.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 19, 9, 19, 19, 19, 19, 19, 19, 19, 18, 29, 29, 19, 29, 29, 29, 29, 29, 29, 28, 39, 39, 39, 29, 39, 39, 39, 39, 39, 38, 49, 49, 49, 49, 39, 49, 49, 49, 49, 48, 59, 59, 59, 59, 59, 49, 59, 59, 59, 58, 69, 69, 69, 69, 69, 69, 59, 69, 69, 68, 79

Offset: 1

Bernard Schott, Oct 29 2022

Note that only when n is pandigital with 0 (A050278, A171102), such m does not exist and a(n) = -1; see examples for smallest pandigital cases.

			a(19) = 8, a(20) = 19; a(21) = 9.
a(123456789) = 0; a(1234567890) = -1.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A050289, A050278, A171102.

Cf. A358097 (similar, with smallest integer m > n).

a[n_] := Module[{d = Complement[Range[0, 9], IntegerDigits[n]], m = n - 1}, If[d == {} || d == {0}, -1, While[m >= 0 && ! AllTrue[IntegerDigits[m], MemberQ[d, #] &], m--]; m]]; Array[a, 100] (* Amiram Eldar, Oct 29 2022 *)

a(n) = my(d=Set(digits(n))); forstep (m=n-1, 0, -1, if (!#setintersect(d, Set(digits(m))), return(m))); return(-1); \\ Michel Marcus, Oct 30 2022

from itertools import product
def a(n):
    s = str(n)
    r = sorted(set("1234567890") - set(s), reverse=True)
    if len(r) == 0: return -1
    if r == ["0"]: return 0
    for d in range(len(s), 0, -1):
        for p in product(r, repeat=d):
            m = int("".join(p))
            if m < n: return m
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Oct 29 2022

a(10^n) = 10^n - 1 for n >= 0.

a(A050289(n))=0.

cp's OEIS Frontend

A030283 a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica

Formula

Extensions