A283986 a(n) = A002487(n-1) OR A002487(n), where OR is bitwise-or (A003986).

1, 1, 3, 3, 3, 3, 3, 3, 5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 7, 7, 11, 13, 7, 7, 7, 7, 13, 11, 7, 7, 5, 5, 7, 7, 13, 13, 15, 15, 15, 11, 11, 11, 13, 13, 13, 15, 15, 11, 11, 15, 15, 13, 13, 13, 11, 11, 11, 15, 15, 15, 13, 13, 7, 7, 7, 7, 15, 15, 15, 15, 13, 13, 15, 15, 27, 23, 23, 27, 15, 15, 15, 15, 27, 27, 29, 29, 31, 23, 21, 29, 31, 23, 23, 25, 11, 11, 11, 11, 25

Offset: 1

Author

Antti Karttunen, Mar 21 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Odd bisection of A283976.

Cf. A002487, A003986, A283988.

Cf. A283973 (positions where coincides with A007306, equally, with A283987).

Programs

Mathematica

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

PARI

A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
for(n=1, 101, print1(bitor(A(n - 1), A(n))", ")) \\ Indranil Ghosh, Mar 23 2017

Python

from functools import reduce
def A283986(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))) # Chai Wah Wu, May 05 2023

Scheme

(define (A283986 n) (A003986bi (A002487 (- n 1)) (A002487 n))) ;; Where A003986bi implements bitwise-OR (A003986).

Formula

a(n) = A002487(n-1) OR A002487(n), where OR is bitwise-or (A003986).

a(n) = A283987(n) + A283988(n).

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

a(n) = A283976((2*n)-1).