A367288 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(n-1) and a(n) are congruent modulo n, and the least value not yet in the sequence appears as soon as possible.

0, 1, 5, 2, 18, 3, 39, 4, 60, 6, 106, 7, 151, 8, 204, 9, 265, 10, 334, 11, 411, 12, 496, 13, 589, 14, 690, 15, 799, 16, 916, 17, 1009, 19, 1175, 20, 1316, 21, 1465, 22, 1622, 23, 1787, 24, 1960, 25, 2141, 26, 2330, 27, 2527, 28, 2732, 29, 2945, 30, 3166, 31

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) and v are congruent modulo 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).

This construction is similar to that of A352713.

This sequence is a variant of A125717 and, by design, is guaranteed to be a permutation of the nonnegative integers (with inverse A367289).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Index entries for sequences related to Recamán's sequence

Index entries for sequences that are permutations of the natural numbers

Example

The first terms are:
  n   a(n)  a(n-1) mod n  a(n) mod n
  --  ----  ------------  ----------
   0     0  N/A           N/A
   1     1             0           0
   2     5             1           1
   3     2             2           2
   4    18             2           2
   5     3             3           3
   6    39             3           3
   7     4             4           4
   8    60             4           4
   9     6             6           6
  10   106             6           6
  11     7             7           7
  12   151             7           7
  13     8             8           8

Prog

(PARI) See Links section.

Crossrefs

Cf. A005132, A125717, A352713, A367289 (inverse), A367290.

Sequence in context: A286161 A286252 A286154 * A304635 A356330 A306198

Adjacent sequences: A367285 A367286 A367287 * A367289 A367290 A367291

Keyword

nonn

Author

Rémy Sigrist, Nov 12 2023

Status

approved