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

1,3

Comments

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

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

Formula

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

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

Example

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  -

Prog

(PARI) See Links section.

Crossrefs

Cf. A002487, A097581.

Sequence in context: A248138 A049234 A299351 * A294299 A125504 A243929

Adjacent sequences: A358932 A358933 A358934 * A358936 A358937 A358938

Keyword

nonn

Author

Rémy Sigrist, Dec 07 2022

Status

approved