A329811 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, 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, 16, 71, 41, 53, 25, 72, 111, 112, 131, 45, 34, 151, 61, 74, 152, 73, 54, 37, 29, 121, 123, 58, 132, 134, 153, 47, 141, 56, 171, 81, 92, 1111, 211, 213, 145, 38, 191

Offset: 1

Author

Eric Angelini and Rémy Sigrist, Nov 21 2019

Keywords

• nonn
• base

Comments

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

All terms are zeroless.

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

Examples

			The first terms, alongside the corresponding (x, y, z), are:
  n   a(n)  x  y  z
  --  ----  -  -  -
   1     1  1  2  3
   2     2  2  3  5
   3     3  3  5  4
   4     5  5  4  9
   5     4  4  9  1
   6     9  9  1  1
   7    11  1  1  1
            1  1  2
   8    12  1  2  1
            2  1  3
   9    13  1  3  1
            3  1  4
  10    14  1  4  1
            4  1  5
  11    15  1  5  6
            5  6  1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the previous term mod 100)
• Rémy Sigrist, PARI program for A329811
• Rémy Sigrist, C# program for A329811

Crossrefs

Cf. A002275, A052382, A085947.

Programs

PARI

See Links section.
(C#) See Links section.