cp's OEIS Frontend

A342072 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.

%I A342072 #11 Mar 01 2021 02:12:33
%S A342072 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 A342072 81,82,86,26,13,19,29,23,43,46,92,32,31,33,36,66,61,62,64,68,38,76,71,
%U A342072 72,74,37,67,127,47,87,167,117,39,69,63,123,113,111,112,56
%N A342072 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 A342072 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 A342072 Apparently, all positive integers appear in this sequence.
%C A342072 Multiples of 5 are clustered.
%H A342072 Rémy Sigrist, <a href="/A342072/b342072.txt">Table of n, a(n) for n = 1..10000</a>
%H A342072 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 A342072 Rémy Sigrist, <a href="/A342072/a342072.gp.txt">PARI program for A342072</a>
%e A342072 The first terms, alongside the substitution that gives a(n+1), are:
%e A342072   n   a(n)  a(n+1)
%e A342072   --  ----  ------
%e A342072    1     1   (1*2)
%e A342072    2     2   (2*2)
%e A342072    3     4   (4*2)
%e A342072    4     8   (8*2)
%e A342072    5    16  1(6/6)
%e A342072    6    11  1(1*2)
%e A342072    7    12  (12/4)
%e A342072    8     3   (3*2)
%e A342072    9     6   (6*3)
%e A342072   10    18  (18/2)
%e A342072   11     9   (9*3)
%e A342072   12    27  (2/2)7
%e A342072   13    17  (17*2)
%e A342072   14    34  (3/3)4
%e A342072   15    14  (14/2)
%o A342072 (PARI) See Links section.
%Y A342072 Cf. A323286.
%K A342072 nonn,base
%O A342072 1,2
%A A342072 _Rémy Sigrist_, Feb 27 2021