A174091 a(n) = n OR 2.

2, 3, 2, 3, 6, 7, 6, 7, 10, 11, 10, 11, 14, 15, 14, 15, 18, 19, 18, 19, 22, 23, 22, 23, 26, 27, 26, 27, 30, 31, 30, 31, 34, 35, 34, 35, 38, 39, 38, 39, 42, 43, 42, 43, 46, 47, 46, 47, 50, 51, 50, 51, 54, 55, 54, 55, 58, 59, 58, 59, 62, 63, 62, 63, 66, 67, 66

Offset: 0

Author

Gary Detlefs, Feb 06 2013

Keywords

• nonn
• easy

Comments

OR(n, 2) + AND(n, 2) = n + 2.

OR(n, 2) - AND(n, 2) = n + 2*(-1)^floor(n/2), A004443.

a(n) = n when n = 2 or 3 mod 4 (n is in A042964). - Alonso del Arte, Feb 07 2013

Examples

			a(3) = 3 because OR(0011, 0010) = 0011 = 3.
a(4) = 6 because OR(0100, 0010) = 0110 = 6.
a(5) = 7 because OR(0101, 0010) = 0111 = 7.
		

Links

• Shane Chern, T. Cai, and H. Zhong, On the cardinality and sum of reciprocals of primitive sequences, Preprint 2018; To appear in Adv. Math. (China).
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Crossrefs

Cf. similar sequences listed in A244587.

Cf. A004443, A042964, A196521.

Programs

Maple

with(Bits): seq(Or(n,2), n=0..60);

Mathematica

Table[BitOr[n, 2], {n, 0, 100}] (* Alonso del Arte, Feb 06 2013 *)
LinearRecurrence[{2,-2,2,-1},{2,3,2,3},80] (* Harvey P. Dale, Oct 25 2016 *)

PARI

a(n)=bitor(n,2) \\ Charles R Greathouse IV, Feb 27 2013

Formula

a(n) = n + 1 + (-1)^floor(n/2).

G.f.: ( 2-x+x^3 ) / ( (1+x^2)*(x-1)^2 ). - R. J. Mathar, Feb 27 2013

Sum_{n>=0} (-1)^n/a(n) = Pi/4 - log(2)/2 = A196521. - Peter McNair, Aug 05 2023