A396346 a(0) = 0; for n > 0, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n - 1.

0, 0, 1, 3, 6, 10, 4, 10, 2, 10, 19, 8, 19, 31, 17, 31, 15, 31, 13, 31, 11, 31, 9, 31, 7, 31, 5, 31, 58, 29, 58, 27, 58, 25, 58, 23, 58, 21, 58, 96, 56, 96, 54, 96, 52, 96, 50, 96, 48, 96, 46, 96, 44, 96, 42, 96, 40, 96, 38, 96, 36, 96, 34, 96, 32, 96, 30, 96, 28, 96, 26, 96, 24

Offset

0,4

Comments

Every natural number appears in the sequence for n >= 2. Specifically, any natural number that is not a term of A396345 appears exactly once, while the terms of A396345 appear at least once.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..8969

Formula

For n >= 3, a(n) = A396345(m) if n - m == 0 mod 2, and a(n) = A396345(m) - n otherwise, where m is the unique index satisfying A396344(m) <= n < A396344(m+1).

Example

  m | a(n) for A396344(m) <= n < A396344(m+1)
----+--------------------------------------------------------------------------------
  - |   0,  0,   1 (for n = 0, 1, 2)
  1 |   3;
  2 |   6;
  3 |  10,  4,  10,  2,  10;
  4 |  19,  8,  19;
  5 |  31, 17,  31, 15,  31, 13,  31, 11,  31,  9,  31,  7,  31,  5,  31;
  6 |  58, 29,  58, 27,  58, 25,  58, 23,  58, 21,  58;
  7 |  96, 56,  96, 54,  96, 52,  96, 50,  96, 48,  96, 46,  96, 44,  96, ... ,  96;
  8 | 181, 94, 181, 92, 181, 90, 181, 88, 181, 86, 181, 84, 181, 82, 181, ... , 181;

Crossrefs

Cf. A005132, A396344, A396345, A396347.

Sequence in context: A329153 A337771 A232175 * A065234 A387683 A333531

Adjacent sequences: A396343 A396344 A396345 * A396347 A396348 A396349

Keyword

nonn,look

Author

Seiichi Manyama, May 23 2026

Status

approved