login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A022441 a(n) = c(n) + c(n-1) where c (A055562) is the sequence of numbers not in a. 4
1, 5, 7, 10, 14, 17, 20, 23, 25, 28, 31, 34, 37, 40, 43, 46, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Ivan Neretin, Table of n, a(n) for n = 0..10000

J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264.

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(n) + a(n-1) = 3n + 2 - (floor(log_2 n) mod 2) for n >= 1. - Jeffrey Shallit, Jun 08 2000

For n>0, a(n) = b(n) with b(0)=0, b(2n) = -b(n)+9n+3, b(2n+1) = -b(n)+9n+6-[n==0]. - Ralf Stephan, Oct 24 2003

a(n) = A210770(2*n+1). - Reinhard Zumkeller, Mar 25 2012

MAPLE

A022441 := n-> `if`(n=0, 1, 3*n + 2 - (ilog2(n) mod 2)):

seq(A022441(n), n= 0..59);

MATHEMATICA

Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2 + 1, #2 + 2}]]] &, {1, 5}, Range[58]] (* Ivan Neretin, Mar 30 2017 *)

Table[If[n==0, 1, 3*n+2 - Mod[Floor[Log[n]/Log[2]], 2]], {n, 0, 30}] (* G. C. Greubel, Mar 08 2018 *)

PROG

(PARI) for(n=0, 30, print1(if(n==0, 1, 3*n+2 - (floor(log(n)/log(2))%2)), ", ")) \\ G. C. Greubel, Mar 08 2018

(Magma) [1] cat [3*n + 2 - (Floor((Log(n)/Log(2))) mod 2): n in [0..10]]; // G. C. Greubel, Mar 08 2018

CROSSREFS

Cf. A055562 (complement), A022424.

Sequence in context: A356218 A354939 A282107 * A156243 A020942 A190035

Adjacent sequences: A022438 A022439 A022440 * A022442 A022443 A022444

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 23 2000

Term a(16)=50 fixed by Ivan Neretin, Mar 30 2017

Updated by Clark Kimberling, Feb 19 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)