A283988 - OEIS

A283988

a(n) = A002487(n-1) AND A002487(n), where AND is bitwise-and (A004198).

0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 4, 4, 3, 0, 0, 5, 2, 2, 5, 0, 0, 3, 4, 4, 1, 0, 4, 1, 0, 0, 3, 2, 2, 3, 8, 8, 5, 4, 4, 1, 0, 0, 1, 4, 4, 5, 8, 8, 3, 2, 2, 3, 0, 0, 1, 4, 0, 1, 6, 2, 1, 4, 8, 9, 4, 4, 11, 2, 2, 1, 0, 8, 1, 2, 10, 3, 0, 0, 5, 0, 0, 1, 0, 0, 3, 0, 0, 9, 2, 2, 9, 0, 0, 3, 0, 0, 1, 0, 0, 5, 0, 0, 3, 10, 2, 1, 8, 0, 1, 2, 2, 11, 4

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OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A002487(n-1) AND A002487(n), where AND is bitwise-and (A004198).

a(n) = A283986(n) - A283987(n).

a(n) = A007306(n) - A283986(n) = (A007306(n) - A283987(n))/2.

a(n) = A283978((2*n)-1).

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ@ n, a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[BitAnd[a[n - 1], a@ n], {n, 120}] (* Michael De Vlieger, Mar 22 2017 *)

PROG

(Scheme) (define (A283988 n) (A004198bi (A002487 (- n 1)) (A002487 n))) ;; Where A004198bi implements bitwise-AND (A004198).

(PARI) A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));

for(n=1, 120, print1(bitand(A(n - 1), A(n)), ", ")) \\ Indranil Ghosh, Mar 23 2017

(Python)

from functools import reduce

def A283988(n): return sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(n)[-1:2:-1], (1, 0)))&sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(n-1)[-1:2:-1], (1, 0))) if n>1 else 0 # Chai Wah Wu, May 05 2023

CROSSREFS

Odd bisection of A283978.

Cf. A002487, A004198, A007306, A283986, A283987.

Cf. A283973 (positions of zeros), A283974 (nonzeros).

Sequence in context: A287320 A210502 A350797 * A276204 A365573 A370278

Adjacent sequences: A283985 A283986 A283987 * A283989 A283990 A283991

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Mar 21 2017

STATUS

approved