A283974 -id:A283974 - cp's OEIS frontend

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

Offset: 1

Antti Karttunen, Mar 21 2017

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Odd bisection of A283978.
Cf. A002487, A004198, A007306, A283986, A283987.
Cf. A283973 (positions of zeros), A283974 (nonzeros).

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 *)

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

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

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

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).

A283973 Numbers n such that A007306(n) = A283986(n); positions of zeros in A283988.

Original entry on oeis.org

1, 3, 4, 9, 10, 12, 13, 15, 16, 21, 22, 27, 28, 33, 36, 37, 48, 49, 60, 61, 64, 78, 84, 85, 87, 88, 90, 91, 93, 94, 99, 100, 102, 103, 105, 106, 108, 109, 115, 129, 130, 133, 135, 136, 141, 144, 145, 153, 159, 160, 162, 171, 172, 189, 190, 192, 193, 195, 196, 213, 214, 223, 225, 226, 232, 240, 241, 244, 249, 250, 252, 255, 256

Offset: 1

Antti Karttunen, Mar 21 2017

Equally, numbers n for which A007306(n) = A283987(n), or equally, numbers n for which A283986(n) = A283987(n).

Numbers n such that the binary representations of A002487(n-1) and A002487(n) have no 1-bits in common shared positions.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to binary expansion of n

Cf. A283974 (complement).

Cf. A002487, A007306, A283986, A283987, A283988.

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ@ n, a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Map[Function[n, If[EvenQ@ n, a[n/2], BitOr[a[#], a[# + 1]] &[(n - 1)/2]]], 2 Range[99] - 1] (* Michael De Vlieger, Mar 22 2017 *)

A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
D(n) = if(n<1, 1, sum(k=0, n, binomial(n + k - 1, 2*k)%2)) /* A007306 */
for(n=1, 300, if(bitor(A(n - 1), A(n)) == D(n), print1(n,", "))) \\ Indranil Ghosh, Mar 23 2017

cp's OEIS Frontend

A283988 a(n) = A002487(n-1) AND A002487(n), where AND is bitwise-and (A004198).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Scheme

Formula