

A317420


a(n) = number of k with 1 <= k <= n1 such that a(k) AND a(nk) = 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
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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..n1} [P(a(k), a(nk))] 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, n1, bitand(a[k], a[nk])==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



