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%I #19 Dec 23 2024 14:53:44
%S 0,1,10,2,11,12,3,13,14,7,15,5,16,4,17,18,6,19,21,23,31,41,51,30,20,
%T 22,24,8,25,35,27,9,29,61,71,81,32,26,28,34,42,33,36,37,91,47,100,40,
%U 38,52,43,101,102,39,53,103,104,44,45,49,57,63,59,105,50,54,46,62,72,48,56,58,82,92,64,68,74,106,107,108,60,55,65,75,73,109,110,85
%N a(n+1) has a digit that divides a(n) and is the least positive integer not appearing earlier with this property.
%C A variant of A248024.
%C This is a permutation of the nonnegative integers, see A257276 for the inverse permutation.
%C There are large ranges of fixed points, e.g., between a(135) = 99 and a(200) = 201, or between a(1080) = 999 and a(2000) = 2001. For indices n in these ranges, the sequence restricted to [0...n] is a permutation (i.e., all numbers up to n appear among the values up to that point).
%C If one requires that a(n+1) has *no* digit dividing a(n), the sequence starts 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 30, 40, 33, 22, 34, ... and stops at a(1422) = 2520, divisible by any digit. If one requires the sequence to be increasing, then it goes ..., 20, 30, 40, 60, 70, 80, 90, 400, 600, 700, 800, 900, 7000, 9000, 70000, 90000, 700000, 900000, ...
%H M. F. Hasler, <a href="/A257277/b257277.txt">Table of n, a(n) for n = 0..1199</a>
%H E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-May/014822.html">Division by digits (variation)</a>, SeqFan list, May 7, 2015.
%o (PARI) {u=n=0;until(print1(n","),u+=1<<n;d=select(i->!(n%i),vector(9,i,i));n=0;until(!bittest(u,n++)&&setintersect(d,Set(digits(n))),))}
%Y Cf. A248024, A257276.
%K nonn,base,look
%O 0,3
%A _Eric Angelini_ and _M. F. Hasler_, May 07 2015