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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.
2
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
1,2
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).
EXAMPLE
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
PROG
(PARI) See Links section.
CROSSREFS
Cf. A262323, A360472 (inverse).
Sequence in context: A071154 A071161 A367609 * A125886 A067574 A365705
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 08 2023
STATUS
approved