A385991 a(n) is the number of distinct values among A002487(0), ..., A002487(n).

1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16

Offset

0,2

Comments

This sequence exhibits large runs of consecutive equal values.

Links

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

Rémy Sigrist, PARI program

Index entries for sequences related to Stern's sequences

Formula

a(A091945(n)) = n (this is the first occurrence of n in the sequence).

a(2*n) = a(2*n-1) for any n > 0.

Example

Sequence begins:
  n   a(n)  A002487(n)
  --  ----  ----------
   0     1           0
   1     2           1
   2     2           1
   3     3           2
   4     3           1
   5     4           3
   6     4           2
   7     4           3
   8     4           1
   9     5           4
  10     5           3
  11     6           5
  12     6           2
  13     6           5
  14     6           3
  15     6           4
  16     6           1
  17     6           5
  18     6           4
  19     7           7

Prog

(PARI) \\ See Links section.
(Python)
def A385991(n):
    if n==0: return 1
    a, b, s, c = 0, 1, {0, 1}, 2
    for i in range(n-1):
        a, b = b, ((a//b<<1)+1)*b-a
        if b not in s:
            c += 1
            s.add(b)
    return c # Chai Wah Wu, Jul 17 2025

Crossrefs

See A061069, A061070 and A061071 for similar sequences.

Cf. A002487, A091945, A385993.

Sequence in context: A071868 A179390 A237819 * A082447 A139789 A366033

Adjacent sequences: A385988 A385989 A385990 * A385992 A385993 A385994

Keyword

nonn

Author

Rémy Sigrist, Jul 14 2025

Status

approved