A371214 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(n-1) + a(n) is a multiple of n, and the least value not yet in the sequence appears as soon as possible.

0, 1, 7, 2, 22, 3, 45, 4, 76, 5, 115, 6, 18, 8, 216, 9, 279, 10, 350, 11, 429, 12, 516, 13, 611, 14, 714, 15, 825, 16, 944, 17, 47, 19, 1205, 20, 1348, 21, 55, 23, 1657, 24, 1824, 25, 1999, 26, 2182, 27, 2373, 28, 2572, 29, 2779, 30, 2994, 31, 3217, 32, 3448

Offset

0,3

Comments

To build the sequence:

- we start with a(0) = 0, and repeatedly:

- let a(n) be the last known term and v the least value not yet in the sequence,

- if a(n) + v is a multiple of n+1 then a(n+1) = v,

- otherwise a(n+2) = v and a(n+1) is chosen as small as possible in such a way as to satisfy the required congruences (this is always possible as n+1 and n+2 are coprime).

The construction is similar to that of A367288.

This sequence is a variant of A099506 and, by design, is guaranteed to be a permutation of the nonnegative integers (with inverse A371215).

Links

Table of n, a(n) for n=0..58.

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms are:
  n   a(n)  (a(n-1) + a(n))/n
  --  ----  -----------------
   0     0  N/A
   1     1                  1
   2     7                  4
   3     2                  3
   4    22                  6
   5     3                  5
   6    45                  8
   7     4                  7
   8    76                 10
   9     5                  9
  10   115                 12
  11     6                 11
  12    18                  2

Prog

(PARI) See Links section.

Crossrefs

Cf. A099506, A367288, A371215 (inverse).

Sequence in context: A279807 A282362 A248282 * A213836 A340801 A338284

Adjacent sequences: A371211 A371212 A371213 * A371215 A371216 A371217

Keyword

nonn

Author

Rémy Sigrist, Mar 15 2024

Status

approved