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A378106 Lexicographically earliest sequence of distinct positive integers such that among two consecutive terms, the least term divides a positive number whose decimal expansion appears in that of the other term.

%I A378106 #7 Nov 17 2024 13:07:40
%S A378106 1,2,4,8,16,3,6,12,24,48,96,9,18,36,72,7,14,28,56,5,10,20,40,80,160,
%T A378106 15,30,60,120,240,480,32,64,128,256,25,50,100,200,400,800,1600,75,150,
%U A378106 300,600,1200,2400,4800,192,19,38,76,152,13,26,52,104,208,416,41
%N A378106 Lexicographically earliest sequence of distinct positive integers such that among two consecutive terms, the least term divides a positive number whose decimal expansion appears in that of the other term.
%C A378106 Will every integer appear in the sequence?
%H A378106 Rémy Sigrist, <a href="/A378106/b378106.txt">Table of n, a(n) for n = 1..10000</a>
%H A378106 Rémy Sigrist, <a href="/A378106/a378106.gp.txt">PARI program</a>
%e A378106 The first terms are:
%e A378106   n   a(n)
%e A378106   --  ----
%e A378106    1     1
%e A378106    2     2
%e A378106    3     4
%e A378106    4     8
%e A378106    5    16
%e A378106    6     3      (3 divides 6, and 6 appears in 16)
%e A378106    7     6
%e A378106    8    12
%e A378106    9    24
%e A378106   10    48
%e A378106   11    96
%e A378106   12     9
%e A378106   13    18
%e A378106   14    36
%e A378106   15    72
%o A378106 (PARI) \\ See Links section.
%Y A378106 See A342072 and A378107 for similar sequences.
%K A378106 nonn,base
%O A378106 1,2
%A A378106 _Rémy Sigrist_, Nov 16 2024