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A218468 a(n+1) is a multiple of at least one digit of a(n); this is the lexicographically earliest injective such sequence.

%I A218468 #44 Dec 23 2024 14:53:43
%S A218468 1,2,4,8,16,3,6,12,5,10,7,14,9,18,11,13,15,17,19,20,22,24,26,28,30,21,
%T A218468 23,27,32,33,36,39,42,34,40,44,48,52,25,35,45,50,55,60,54,56,65,66,72,
%U A218468 38,51,29,46,64,68,78,49,63,57,70,77,84,76,90,81,31,37,69,96,99,108,41,43,75,80,88,104,47,91,53,85,95,100,58,105,59,110,61,62
%N A218468 a(n+1) is a multiple of at least one digit of a(n); this is the lexicographically earliest injective such sequence.
%C A218468 "Lexicographically earliest injective sequence" means that a(n+1) is the least positive integer not occurring earlier with the given property.
%C A218468 Conjectured to be a permutation of the positive integers, which is the case if and only if an infinite number of terms have a digit "1".
%C A218468 Conjecture: For nonnegative integer x, 2*10^x appears at index 2*10^x (see A226179). _Hans Havermann_, May 29 2013
%C A218468 Fixed points, i.e., indices n for which a(n)=n, are listed in A226179. - _M. F. Hasler_, May 30 2013
%C A218468 B. Jubin and H. Havermann made remarks about this sequence in other bases, its fractal nature and fixed points: See the link to the SeqFan list. - _M. F. Hasler_, May 30 2013
%H A218468 Paul Tek, <a href="/A218468/b218468.txt">Table of n, a(n) for n = 1..10000</a>
%H A218468 B. Jubin and others, in reply to E. Angelini's post <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-May/011230.html">a(n+1) is the multiple of at least one digit of a(n)</a>, SeqFan list, May 29 2013.
%o A218468 (PARI) A218468(n,a=[1])={ for(n=1,n-1,print1(a[#a]",");my(d=digits(a[#a])); for(k=2,9e9,setsearch(Set(a),k) || for(i=1,#d,!d[i] || k%d[i] || !(a=concat(a,k)) || next(3))));a[#a]} \\ could be optimized...
%K A218468 nonn,base
%O A218468 1,2
%A A218468 _Eric Angelini_ and _M. F. Hasler_, May 28 2013