A163617 a(2*n) = 2*a(n), a(2*n + 1) = 2*a(n) + 2 + (-1)^n, for all n in Z.

0, 3, 6, 7, 12, 15, 14, 15, 24, 27, 30, 31, 28, 31, 30, 31, 48, 51, 54, 55, 60, 63, 62, 63, 56, 59, 62, 63, 60, 63, 62, 63, 96, 99, 102, 103, 108, 111, 110, 111, 120, 123, 126, 127, 124, 127, 126, 127, 112, 115, 118, 119, 124, 127, 126, 127, 120, 123, 126, 127, 124, 127, 126

Offset

0,2

Comments

Fibbinary numbers (A003714) give all integers n >= 0 for which a(n) = 3*n.

From Antti Karttunen, Feb 21 2016: (Start)

Fibbinary numbers also give all integers n >= 0 for which a(n) = A048724(n).

Note that there are also other multiples of three in the sequence, for example, A163617(99) = 231 ("11100111" in binary) = 3*77, while 77 ("1001101" in binary) is not included in A003714. Note that 99 is "1100011" in binary.

(End)

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(n) = -A163618(-n) for all n in ZZ.

Conjecture: a(n) = A003188(n) + (6*n + 1 - (-1)^n)/4. - Velin Yanev, Dec 17 2016

Example

G.f. = 3*x + 6*x^2 + 7*x^3 + 12*x^4 + 15*x^5 + 14*x^6 + 15*x^7 + 24*x^8 + 27*x^9 + ...

Maple

A163617 := n -> Bits:-Or(2*n, n):
seq(A163617(n), n=0..62); # Peter Luschny, Sep 23 2019

Mathematica

Table[BitOr[n, 2*n], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

Prog

(PARI) {a(n) = bitor(n, n<<1)};
(PARI) {a(n) = if( n==0 || n==-1, n, 2 * a(n \ 2) + (n%2) * (2 + (-1)^(n \ 2)))};
(Haskell)
import Data.Bits ((.|.), shiftL)
a163617 n = n .|. shiftL n 1 :: Integer
-- Reinhard Zumkeller, Mar 06 2013
(Scheme) (define (A163617 n) (A003986bi n (+ n n))) ;; Here A003986bi implements dyadic bitwise-OR operation (see A003986) - Antti Karttunen, Feb 21 2016
(Julia)
using IntegerSequences
A163617List(len) = [Bits("OR", n, n<<1) for n in 0:len]
println(A163617List(62))  # Peter Luschny, Sep 26 2021

Crossrefs

Cf. A003986, A048724, A213370, A163618.

Cf. also A269161.

Sequence in context: A335431 A269174 A161903 * A189634 A371218 A047705

Adjacent sequences: A163614 A163615 A163616 * A163618 A163619 A163620

Keyword

nonn

Author

Michael Somos, Aug 01 2009

Extensions

Comment about Fibbinary numbers rephrased by Antti Karttunen, Feb 21 2016

Status

approved