A174091 -id:A174091 - cp's OEIS frontend

A244587 a(n) = n OR 5.

5, 5, 7, 7, 5, 5, 7, 7, 13, 13, 15, 15, 13, 13, 15, 15, 21, 21, 23, 23, 21, 21, 23, 23, 29, 29, 31, 31, 29, 29, 31, 31, 37, 37, 39, 39, 37, 37, 39, 39, 45, 45, 47, 47, 45, 45, 47, 47, 53, 53, 55, 55, 53, 53, 55, 55, 61, 61, 63, 63, 61, 61, 63, 63, 69, 69, 71, 71

Offset: 0

Gary Detlefs, Jun 30 2014

Cf. similar sequences of the type n OR k: A109613 (k=1), A174091 (k=2), A244584 (k=3), A244586 (k=4), this sequence (k=5), A244588 (k=6).

[BitwiseOr(n, 5): n in [0..80]]; // Bruno Berselli, Jul 01 2014

Maple
```
with(Bits): seq(Or(n,5), n = 0..60);
```

a(n) = bitor(n, 5); \\ Michel Marcus, Jan 19 2023

def A244587(n): return n|5 # Chai Wah Wu, Jan 18 2023

a(n) = (n+5) - (n AND 5).
a(n) = (n XOR 5) + (n AND 5).
a(n) = n +((n+1) mod 2)+4*floor(((n+4) mod 8)/4).
a(n) = (2*n + 4*(-1)^floor(n/4) + (-1)^n + 5)/2. - Bruno Berselli, Jul 01 2014
G.f.: (x^6+x^4-3*x^2+5)/((x+1)*(x^4+1)*(x-1)^2). - Alois P. Heinz, Jul 01 2014

Some terms corrected by Bruno Berselli, Jul 01 2014

A382865 Bitwise XOR of all integers between n and 2n (endpoints included).

Original entry on oeis.org

0, 3, 5, 4, 8, 15, 13, 8, 16, 27, 21, 28, 24, 23, 29, 16, 32, 51, 37, 52, 40, 63, 45, 56, 48, 43, 53, 44, 56, 39, 61, 32, 64, 99, 69, 100, 72, 111, 77, 104, 80, 123, 85, 124, 88, 119, 93, 112, 96, 83, 101, 84, 104, 95, 109, 88, 112, 75, 117, 76, 120, 71, 125, 64, 128, 195

Offset: 0

Federico Provvedi, May 21 2025

			a(3) = 3 XOR 4 XOR 5 XOR 6 = 4, in binary representation is: ((011 XOR 100) XOR 101) XOR 110 = (111 XOR 101) XOR 110 = 010 XOR 110 = 100 (4 in decimal).

Alois P. Heinz, Table of n, a(n) for n = 0..16383
Karl-Heinz Hofmann, Zoom trip with n mod 4 colored.
Wikipedia, Bitwise operation: XOR

Cf. A038712, A047615, A065621, A114389, A010873, A048724, A174091, A181983.

a:= proc(n) option remember; uses Bits; `if`(n=0, 0,
      Xor(Xor(Xor(a(n-1), n-1), 2*n-1), 2*n))
    end:
seq(a(n), n=0..65);  # Alois P. Heinz, May 26 2025

a[n_] = BitXor[BitOr[n-1, 2] - (-1)^n*(n-1), 4*n]/2; Table[a[n],{n,0, 65}]

a(n) = my(b=n); for (i=n+1, 2*n, b = bitxor(b, i)); b; \\ Michel Marcus, May 25 2025

def A382865(n): return [0, n, 1, n-1][n%4] ^ (2*n) # Karl-Heinz Hofmann, May 26 2025

a(2n) = A047615(n+1), and for every integer k>1: a(n*2^k -1) = 2^k * A065621(n).
a(4n) = 8*n, a(4n+1) = 2*A114389(n+1) + 1, a(4n+2) = 8*n + 5, a(4n+3) = 4*A065621(n+1).
From Karl-Heinz Hofmann, May 27 2025: (Start)
For all n == 0 (mod 4) --> a(n) = A005843(n) = 2*n
For all n == 1 (mod 4) --> a(n) = A048724(n)
For all n == 2 (mod 4) --> a(n) = A005408(n) = 2*n + 1
For all n == 3 (mod 4) --> a(n) = A048724(n) - 1 (End)
a(n) = (1/2) * XOR(A174091(n-1) - A181983(n-1), 4*n). - Federico Provvedi, May 31 2025

cp's OEIS Frontend

A244587 a(n) = n OR 5.

Views

Author

Keywords

Crossrefs

Programs

Magma

Maple

PARI

Python

Formula

Extensions