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Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, a(n+1) can be obtained by replacing in the decimal representation of a(n) some nonempty substring m (without leading zero) by a divisor of m or by a positive multiple of m.
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%I #11 Mar 01 2021 02:12:33

%S 1,2,4,8,16,11,12,3,6,18,9,27,17,34,14,7,21,22,24,28,48,41,42,44,84,

%T 81,82,86,26,13,19,29,23,43,46,92,32,31,33,36,66,61,62,64,68,38,76,71,

%U 72,74,37,67,127,47,87,167,117,39,69,63,123,113,111,112,56

%N Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, a(n+1) can be obtained by replacing in the decimal representation of a(n) some nonempty substring m (without leading zero) by a divisor of m or by a positive multiple of m.

%C The procedure used to generate the terms of this sequence has similarities with that described in A323286 (Choix de Bruxelles); however here, we don't limit ourselves to divide or multiply by two.

%C Apparently, all positive integers appear in this sequence.

%C Multiples of 5 are clustered.

%H Rémy Sigrist, <a href="/A342072/b342072.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A342072/a342072.png">Colored scatterplot of the first 10000 terms</a> (red pixels correspond to five clusters of multiples of 5)

%H Rémy Sigrist, <a href="/A342072/a342072.gp.txt">PARI program for A342072</a>

%e The first terms, alongside the substitution that gives a(n+1), are:

%e n a(n) a(n+1)

%e -- ---- ------

%e 1 1 (1*2)

%e 2 2 (2*2)

%e 3 4 (4*2)

%e 4 8 (8*2)

%e 5 16 1(6/6)

%e 6 11 1(1*2)

%e 7 12 (12/4)

%e 8 3 (3*2)

%e 9 6 (6*3)

%e 10 18 (18/2)

%e 11 9 (9*3)

%e 12 27 (2/2)7

%e 13 17 (17*2)

%e 14 34 (3/3)4

%e 15 14 (14/2)

%o (PARI) See Links section.

%Y Cf. A323286.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Feb 27 2021