A184992 a(n) is the least positive integer not occurring earlier that shares a digit with a(n-1); a(1)=1.

1, 10, 11, 12, 2, 20, 21, 13, 3, 23, 22, 24, 4, 14, 15, 5, 25, 26, 6, 16, 17, 7, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70, 71, 72, 73

Offset: 1

Author

Eric Angelini, Dec 22 2011

Keywords

• nonn
• base

Comments

A permutation of the positive integers.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A162501, A076654, A130571.

a(n) = A107353(n) for n>=3. - Alois P. Heinz, Dec 22 2011

Cf. A227118 (inverse); A067581.

Programs

Haskell

import Data.List (delete, intersect); import Data.Function (on)
a184992 n = a184992_list !! (n-1)
a184992_list = 1 : f 1 [2..] where
   f u vs = v : f v (delete v vs)
     where v : _ = filter (not . null . (intersect `on` show) u) vs
-- Reinhard Zumkeller, Jul 01 2013

Mathematica

FromDigits /@ Nest[Function[a, Append[a, Block[{k = 2, d}, While[Nand[FreeQ[a, #], IntersectingQ[a[[-1]], #]] &@ Set[d, IntegerDigits@ k], k++]; d]]], {{1}}, 73] (* Michael De Vlieger, Mar 17 2018 *)

PARI

A184992(n,show=0)={my(a=1,u=2^1);for(k=2,n,show && print1(a",");a=Set(Vec(Str(a))); for(j=2,9e9,bittest(u,j) && next;setintersect(Set(Vec(Str(j))),a) || next; u+=2^a=j; break));a}  \\ M. F. Hasler, Dec 22 2011

Python

from itertools import count, islice
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 1
    while True:
        yield an
        digset = set(str(an))
        an = next(k for k in count(mink) if k not in aset and set(str(k))&digset)
        aset.add(an)
        while mink in aset: mink += 1
print(list(islice(agen(), 74))) # Michael S. Branicky, Oct 03 2024