A371220 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(1) + ... + a(n) is a multiple of n, and the least value not yet in the sequence appears as soon as possible.

1, 3, 2, 10, 4, 52, 5, 43, 6, 54, 7, 65, 8, 76, 9, 103, 11, 99, 12, 110, 13, 121, 14, 132, 15, 143, 16, 154, 17, 165, 18, 176, 19, 187, 20, 198, 21, 209, 22, 220, 23, 231, 24, 242, 25, 253, 26, 264, 27, 275, 28, 286, 29, 297, 30, 308, 31, 319, 32, 330, 33, 341

Offset

1,2

Comments

To build the sequence:

- we start with a(1) = 1,

- once we have n terms, let v be the least value not yet in the sequence,

- if a(1) + ... 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 so as to meet the required conditions (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 A019444 and, by design, is guaranteed to be a permutation of the nonnegative integers (with inverse A371221).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the average of the first terms, are:
  n   a(n)  (a(1)+...+a(n))/n
  --  ----  -----------------
   1     1                  1
   2     3                  2
   3     2                  2
   4    10                  4
   5     4                  4
   6    52                 12
   7     5                 11
   8    43                 15
   9     6                 14
  10    54                 18
  11     7                 17
  12    65                 21

Prog

(PARI) See Links section.

Crossrefs

Cf. A019444, A367288, A371221 (inverse).

Sequence in context: A090780 A184174 A277821 * A318280 A057977 A063549

Adjacent sequences: A371217 A371218 A371219 * A371221 A371222 A371223

Keyword

nonn

Author

Rémy Sigrist, Mar 15 2024

Status

approved