A359050 a(n) is the least k such that fusc(k) + fusc(k+1) = n, where "fusc" is Stern's diatomic series (A002487).

0, 1, 2, 4, 5, 16, 9, 10, 17, 19, 18, 22, 21, 34, 36, 46, 38, 37, 41, 94, 42, 70, 69, 76, 75, 73, 77, 133, 74, 82, 86, 139, 137, 85, 141, 157, 138, 268, 162, 148, 146, 289, 150, 154, 182, 166, 149, 283, 165, 169, 276, 274, 281, 637, 170, 292, 282, 307, 314

Offset

1,3

Comments

This sequence is well defined:

- a(1) = 0,

- for any n > 1, 1/(n-1) is in reduced form, so fusc(k) = 1 and fusc(k+1) = n-1 for some k, and a(n) <= k.

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

A002487(a(n)) + A002487(a(n)+1) = n.

Example

The first terms are:
  n    a(n)   fusc(a(n))  fusc(a(n)+1)
  ---  -----  ----------  ------------
    1      0           0             1
    2      1           1             1
    3      2           1             2
    4      4           1             3
    5      5           3             2
    6     16           1             5
    7      9           4             3
    8     10           3             5
    9     17           5             4
   10     19           7             3

Prog

(PARI) See Links section.
(Python)
def A359050(n):
    f, g, k = 0, 1, 0
    while f+g-n:
        k += 1
        m, a = k+1, [1, 0]
        while m:
            a[m&1] = sum(a)
            m >>=1
        f, g = g, a[1]
    return k # Chai Wah Wu, Dec 16 2022

Crossrefs

Cf. A002487.

Sequence in context: A370959 A328230 A229131 * A071316 A056401 A056406

Adjacent sequences: A359047 A359048 A359049 * A359051 A359052 A359053

Keyword

nonn,look

Author

Rémy Sigrist, Dec 14 2022

Status

approved