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%I #6 Mar 12 2019 22:30:44
%S 1,3,1,4,6,3,1,7,8,4,9,6,3,1,11,12,13,14,7,15,16,8,4,17,18,9,6,3,1,19,
%T 21,22,11,23,24,12,26,13,27,28,14,7,29,30,15,31,32,16,8,4,33,34,17,35,
%U 36,18,9,6,3,1,37,38,19,39,40,41,42,21,43,44,22,11,45,46,23,47,48,24,12,49,51,52,26,13,53,54,27,55,56,28,14,7
%N An irregular fractal sequence: underline a(n) iff the concatenation [a(n-1);a(n)] is divisible by a(n); all underlined terms rebuild the starting sequence.
%C The sequence S starts with a(1) = 1 and a(2) = 3. S is extended by duplicating the first term A among the not yet duplicated terms, under the condition that the concatenation [last term Z of the sequence;A] is divisible by A. If this is not the case, we then extend S with the smallest integer X not yet present in S such that the concatenation [last term Z of the sequence;X] is not divisible by X. This is the lexicographically first sequence with this property. The terms 2 and 5 will never appear.
%H Jean-Marc Falcoz, <a href="/A306804/b306804.txt">Table of n, a(n) for n = 1..10002</a>
%e S starts with a(1) = 1 and a(2) = 3
%e Can we duplicate a(1) to form a(3)? Yes, as [31] is divisible by 1, of course; thus a(3) = 1.
%e Can we duplicate a(2) to form a(4)? No, as [13] is not divisible by 3; we thus extend S with the smallest integer X not yet in S such that [a(3);X] is not divisible by X. We get X = 4 and thus a(4) = 4.
%e Can we duplicate a(2) to form a(5)? No, as [43] is not divisible by 3; we thus extend S with the smallest integer X not yet in S such that [a(4);X] is not divisible by X. We get X = 6 and thus a(5) = 6.
%e Can we duplicate a(2) to form a(6)? Yes, as [63] is divisible by 3, of course; thus a(6) = 3.
%e Can we duplicate a(3) to form a(7)? Yes, as [31] is divisible by 1, of course; thus a(7) = 1.
%e Can we duplicate a(4) to form a(8)? No, as [14] is not divisible by 4; we thus extend S with the smallest integer X not yet in S such that [a(7);X] is not divisible by X. We get X = 7 and thus a(8) = 7.
%e Can we duplicate a(4) to form a(9)? No, as [74] is not divisible by 4; we thus extend S with the smallest integer X not yet in S such that [a(8);X] is not divisible by X. We get X = 8 and thus a(9) = 8.
%e Can we duplicate a(4) to form a(10)? Yes, as [84] is divisible by 4, of course; thus a(10) = 4.
%e Etc.
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 11 2019
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