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A257277 a(n+1) has a digit that divides a(n) and is the least positive integer not appearing earlier with this property.

%I A257277 #19 Dec 23 2024 14:53:44
%S A257277 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 A257277 22,24,8,25,35,27,9,29,61,71,81,32,26,28,34,42,33,36,37,91,47,100,40,
%U A257277 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 A257277 a(n+1) has a digit that divides a(n) and is the least positive integer not appearing earlier with this property.
%C A257277 A variant of A248024.
%C A257277 This is a permutation of the nonnegative integers, see A257276 for the inverse permutation.
%C A257277 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 A257277 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 A257277 M. F. Hasler, <a href="/A257277/b257277.txt">Table of n, a(n) for n = 0..1199</a>
%H A257277 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 A257277 (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 A257277 Cf. A248024, A257276.
%K A257277 nonn,base,look
%O A257277 0,3
%A A257277 _Eric Angelini_ and _M. F. Hasler_, May 07 2015