A338802 a(n) is the number of distinct k in the range 1..n such that A000002(k) = A000002(n+1-k).

1, 0, 1, 4, 3, 0, 5, 4, 3, 8, 5, 2, 11, 8, 1, 12, 11, 4, 11, 16, 5, 12, 15, 4, 13, 20, 7, 16, 23, 4, 17, 22, 9, 18, 23, 12, 23, 24, 7, 24, 27, 8, 25, 32, 15, 28, 29, 12, 29, 28, 15, 34, 31, 16, 37, 32, 15, 36, 31, 16, 41, 36, 19, 48, 37, 6, 51, 40, 9, 52, 43

Offset

1,4

Comments

Graphically, we have a superposition of 3 curves; these correspond to the trisections (see scatterplot in Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 2^13 terms (where the color is function of n mod 3)

Rémy Sigrist, PARI program for A338802

Example

For n = 5:
- Kolakoski sequence (K) starts: 1, 2, 2, 1, 1,
- K(1) = K(5),
- K(2) <> K(4),
- K(3) = K(3),
- K(4) <> K(2),
- K(5) = K(1),
- so a(5) = 3.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000002.

Sequence in context: A330392 A204694 A304030 * A242721 A251610 A021703

Adjacent sequences: A338799 A338800 A338801 * A338803 A338804 A338805

Keyword

nonn

Author

Rémy Sigrist, Nov 10 2020

Status

approved