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

Author

Rémy Sigrist, Jul 14 2025

Keywords

• nonn

Comments

This sequence exhibits large runs of consecutive equal values.

Examples

			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
		

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

Crossrefs

See A061069, A061070 and A061071 for similar sequences.

Cf. A002487, A091945, A385993.

Programs

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

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.