A360470 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the k rightmost digits of a(n+1) equal the k leftmost digits of a(n) for some k > 0.

1, 11, 21, 2, 12, 31, 3, 13, 41, 4, 14, 51, 5, 15, 61, 6, 16, 71, 7, 17, 81, 8, 18, 91, 9, 19, 101, 10, 110, 111, 121, 112, 131, 113, 141, 114, 151, 115, 161, 116, 171, 117, 181, 118, 191, 119, 201, 20, 22, 32, 23, 42, 24, 52, 25, 62, 26, 72, 27, 82, 28, 92

Offset: 1

Author

Rémy Sigrist, Feb 08 2023

Keywords

• nonn
• base

Comments

Leading zeros are ignored.

This sequence is a permutation of the positive integers with inverse A360472:

- if a(n) < 10^e, then we can extend the sequence with a number of the form a(n) + k * 10^e (with k > 0),

- by the pigeonhole principle, there are infinitely many terms starting with the same nonzero digit, say with d,

- every number of the form 10*k + d (with k >= 0) appears in the sequence,

- any number v can appear after a term of the form v * 10^k + d (with k > 0).

Examples

			The first terms are:
  n   a(n)  a(n) aligned
  --  ----  ------------
   1     1             1
   2    11            11
   3    21           21
   4     2           2
   5    12          12
   6    31         31
   7     3         3
   8    13        13
   9    41       41
  10     4       4
  11    14      14
  12    51     51
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 1000000 terms
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A262323, A360472 (inverse).

Programs

PARI

See Links section.