A358935 a(n) is the least k > 0 such that fusc(n) = fusc(n + k) or fusc(n) = fusc(n - k) (provided that n - k >= 0), where "fusc" is Stern's diatomic series (A002487).

1, 1, 3, 2, 2, 3, 2, 4, 6, 3, 2, 6, 2, 4, 3, 8, 4, 3, 4, 6, 6, 4, 2, 12, 2, 4, 6, 8, 4, 6, 3, 16, 30, 3, 12, 6, 4, 8, 18, 12, 4, 12, 10, 8, 6, 4, 2, 24, 2, 4, 6, 8, 10, 12, 4, 16, 18, 7, 4, 12, 9, 6, 3, 32, 7, 3, 7, 6, 12, 9, 8, 12, 46, 7, 12, 11, 12, 21, 7

Offset: 1

Author

Rémy Sigrist, Dec 07 2022

Keywords

• nonn

Comments

Every positive integer appears infinitely many times in A002487, hence the sequence is well defined.

Examples

			The first terms, alongside fusc(n) and the direction where to find the same value, are:
  n   a(n)  fusc(n)  dir
  --  ----  -------  ---
   1     1        1  +
   2     1        1  -
   3     3        2  +
   4     2        1  -
   5     2        3  +
   6     3        2  -
   7     2        3  -
   8     4        1  -
   9     6        4  +
  10     3        3  -
  11     2        5  +
  12     6        2  -
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487, A097581.

Programs

PARI

See Links section.

Formula

a(2^k) = 2^(k-1) for any k > 0.

a(n) = 2 iff n belongs to A097581 \ {2}.