A283987 a(n) = A002487(n-1) XOR A002487(n), where XOR is bitwise-xor (A003987).

1, 0, 3, 3, 2, 1, 1, 2, 5, 7, 6, 7, 7, 6, 7, 5, 4, 1, 3, 4, 11, 13, 2, 5, 5, 2, 13, 11, 4, 3, 1, 4, 7, 3, 12, 13, 15, 12, 13, 9, 8, 3, 5, 8, 9, 11, 14, 11, 11, 14, 11, 9, 8, 5, 3, 8, 9, 13, 12, 15, 13, 12, 3, 7, 6, 1, 13, 14, 11, 7, 4, 9, 11, 4, 25, 21, 22, 27, 7, 14, 13, 5, 24, 27, 29, 24, 31, 23, 20, 29, 31, 20, 23, 25, 2, 9, 9, 2, 25, 23, 20, 31, 29, 20, 23

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences related to binary expansion of n

Formula

a(n) = A002487(n-1) XOR A002487(n), where XOR is bitwise-xor (A003987).

a(n) = A283986(n) - A283988(n).

a(n) = A007306(n) - 2*A283988(n).

a(n) = A283977((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[BitXor[a[n - 1], a@ n], {n, 120}] (* Michael De Vlieger, Mar 22 2017 *)

Prog

(Scheme) (define (A283987 n) (A003987bi (A002487 (- n 1)) (A002487 n))) ;; Where A003987bi implements bitwise-XOR (A003987).
(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(bitxor(A(n - 1), A(n)), ", ")) \\ Indranil Ghosh, Mar 23 2017
(Python)
from functools import reduce
def A283987(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 1 # Chai Wah Wu, May 05 2023

Crossrefs

Odd bisection of A283977.

Cf. A002487, A003987, A283988.

Cf. A283973 (positions where coincides with A007306, or equally, with A283986).

Sequence in context: A016455 A278702 A060574 * A286443 A075522 A186144

Adjacent sequences: A283984 A283985 A283986 * A283988 A283989 A283990

Keyword

nonn,base

Author

Antti Karttunen, Mar 21 2017

Status

approved