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A317420 a(n) = number of k with 1 <= k <= n-1 such that a(k) AND a(n-k) = a(k) (where AND denotes the bitwise AND operator). 7
0, 1, 1, 2, 3, 2, 2, 3, 2, 5, 5, 5, 9, 6, 6, 5, 2, 4, 3, 3, 8, 8, 8, 8, 5, 8, 7, 9, 6, 5, 4, 6, 5, 5, 7, 11, 8, 7, 8, 7, 13, 10, 15, 16, 16, 18, 14, 9, 15, 15, 11, 14, 11, 12, 13, 14, 12, 17, 16, 18, 18, 14, 16, 15, 18, 14, 17, 14, 16, 17, 15, 17, 18, 17, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This sequence was inspired by A055224.

See also A317419, A317441, A317443 and A317585 for similar sequences; these sequences can be defined as a(n) = Sum_{k=1..n-1} [P(a(k), a(n-k))] for some predicate P in two variables (where [] is an Iverson bracket).

LINKS

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

EXAMPLE

For n = 4:

- a(1) AND a(3) = 0 AND 1 = 0 = a(1),

- a(2) AND a(2) = 1 AND 1 = 1 = a(2),

- a(3) AND a(1) = 1 AND 0 = 0 <> a(3),

- hence a(4) = 2.

PROG

(PARI) a = vector(75); for (n=1, #a, a[n] = sum(k=1, n-1, bitand(a[k], a[n-k])==a[k]); print1 (a[n] ", "))

CROSSREFS

Cf. A055224, A317419, A317441, A317443, A317585.

Sequence in context: A241604 A282900 A126014 * A256795 A273404 A281976

Adjacent sequences:  A317417 A317418 A317419 * A317421 A317422 A317423

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jul 27 2018

STATUS

approved

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Last modified February 19 10:24 EST 2019. Contains 320310 sequences. (Running on oeis4.)