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Lexicographically earliest sequence of distinct positive integers such that for any consecutive triple of digits, say (x, y, z), x+y is a multiple of z.
1

%I #14 Nov 22 2019 16:25:30

%S 1,2,3,5,4,9,11,12,13,14,15,6,17,8,19,21,31,23,51,32,57,18,91,52,7,35,

%T 16,71,41,53,25,72,111,112,131,45,34,151,61,74,152,73,54,37,29,121,

%U 123,58,132,134,153,47,141,56,171,81,92,1111,211,213,145,38,191

%N Lexicographically earliest sequence of distinct positive integers such that for any consecutive triple of digits, say (x, y, z), x+y is a multiple of z.

%C This sequence is infinite as we can always extend it with a repunit not yet used.

%C All terms are zeroless.

%C 113 is the first zeroless number that cannot appear in this sequence.

%H Rémy Sigrist, <a href="/A329811/b329811.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A329811/a329811.png">Colored scatterplot of the first 100000 terms</a> (where the color is function of the previous term mod 100)

%H Rémy Sigrist, <a href="/A329811/a329811_1.gp.txt">PARI program for A329811</a>

%H Rémy Sigrist, <a href="/A329811/a329811.txt">C# program for A329811</a>

%e The first terms, alongside the corresponding (x, y, z), are:

%e n a(n) x y z

%e -- ---- - - -

%e 1 1 1 2 3

%e 2 2 2 3 5

%e 3 3 3 5 4

%e 4 5 5 4 9

%e 5 4 4 9 1

%e 6 9 9 1 1

%e 7 11 1 1 1

%e 1 1 2

%e 8 12 1 2 1

%e 2 1 3

%e 9 13 1 3 1

%e 3 1 4

%e 10 14 1 4 1

%e 4 1 5

%e 11 15 1 5 6

%e 5 6 1

%o (PARI) See Links section.

%o (C#) See Links section.

%Y Cf. A002275, A052382, A085947.

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Rémy Sigrist_, Nov 21 2019