A389875 Arrangement of numbers such that every digit rotation of the number n is included in descending order after those of n-1.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 11, 21, 12, 31, 13, 41, 14, 51, 15, 61, 16, 71, 17, 81, 18, 91, 19, 20, 2, 21, 12, 22, 22, 32, 23, 42, 24, 52, 25, 62, 26, 72, 27, 82, 28, 92, 29, 30, 3, 31, 13, 32, 23, 33, 33, 43, 34, 53, 35

Offset

0,3

Comments

This sequence is obtained by taking the same definition as A389420, except that the rotations of each number are listed in descending order instead.

Sequence can also be seen as an irregular table, where the n-th row corresponds to the all rotations of the digits of n, sorted in nonascending order. - Michael S. Branicky, Oct 18 2025

Links

Paolo Xausa, Table of n, a(n) for n = 0..10893 (rows 0..3000 of triangle flattened).

Example

At n = 10, the rotations are 01 and 10, so 10 and 1 are appended.
At n = 453, the rotations are 345, 453 and 543 so 543, 453 and 345 are appended.
The first 20 rows are as follows:
  0  | 0
  1  | 1
  2  | 2
  3  | 3
  4  | 4
  5  | 5
  6  | 6
  7  | 7
  8  | 8
  9  | 9
  10 | 10, 1
  11 | 11, 11
  12 | 21, 12
  13 | 31, 13
  14 | 41, 14
  15 | 51, 15
  16 | 61, 16
  17 | 71, 17
  18 | 81, 18
  19 | 91, 19
  20 | 20, 2

Mathematica

A389875row[n_] := ReverseSort[ Map[FromDigits, NestList[RotateLeft, #, Length[#] - 1]]] & [IntegerDigits[n]];
Array[A389875row, 50, 0] (* Paolo Xausa, Oct 23 2025 *)

Prog

(Python)
from itertools import count, islice
def agen():
    for n in count(0):
        s = str(n)
        yield from sorted((int(s[i:] + s[:i]) for i in range(len(s))), reverse=True)
print(list(islice(agen(), 62)))
# after Michael S. Branicky in A389420

Crossrefs

Cf. A055642 (row lengths), A389882 (row sums).

Cf. A389420.

Sequence in context: A381963 A373211 A346393 * A380298 A360074 A392597

Adjacent sequences: A389872 A389873 A389874 * A389876 A389877 A389878

Keyword

nonn,base,tabf,easy,look

Author

Aitzaz Imtiaz, Oct 18 2025

Status

approved