login
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
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
1,2
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.
LINKS
Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the previous term mod 100)
Rémy Sigrist, C# program for A329811
EXAMPLE
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
PROG
(PARI) See Links section.
(C#) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Rémy Sigrist, Nov 21 2019
STATUS
approved