A374530 Lexicographically earliest permutation of the nonnegative terms such that the absolute difference between the rightmost digit of a(n) and the leftmost digit of a(n+1) is the smallest possible one.

0, 1, 10, 11, 12, 2, 20, 13, 3, 30, 14, 4, 40, 15, 5, 50, 16, 6, 60, 17, 7, 70, 18, 8, 80, 19, 9, 90, 100, 101, 102, 21, 103, 31, 104, 41, 105, 51, 106, 61, 107, 71, 108, 81, 109, 91, 110, 111, 112, 22, 23, 32, 24, 42, 25, 52, 26, 62, 27, 72, 28, 82, 29, 92, 200, 113, 33, 34, 43, 35, 53, 36, 63, 37, 73

Offset

1,3

Comments

The mentioned absolute differences are always < 2.

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Example

The digits touching the 1st comma (0 and 1) have an absolute difference of 1;
The digits touching the 2nd comma (1 and 1) have an absolute difference of 0;
The digits touching the 3rd comma (0 and 1) have an absolute difference of 1;
The digits touching the 4th comma (1 and 1) have an absolute difference of 0;
The digits touching the 5th comma (2 and 2) have an absolute difference of 0;
The digits touching the 6th comma (2 and 2) have an absolute difference of 0;
The digits touching the 7th comma (0 and 1) have an absolute difference of 1;
The digits touching the 8th comma (3 and 3) have an absolute difference of 0;
The digits touching the 9th comma (3 and 3) have an absolute difference of 0; etc.

Prog

(Python)
from itertools import count
a = [0]
while len(a) < 30: a.append(next(k for k in count() if k not in a and ((r:=a[-1]%10)==(l:=int(str(k)[0])) or ((r, l)==(0, 1)))))
print(a) # Dominic McCarty, Mar 24 2025

Crossrefs

Cf. A374504, A076654.

Sequence in context: A097585 A063671 A330024 * A184992 A162501 A286890

Adjacent sequences: A374527 A374528 A374529 * A374531 A374532 A374533

Keyword

base,nonn

Author

Eric Angelini, Jul 10 2024

Status

approved