A022441 a(n) = c(n) + c(n-1) where c (A055562) is the sequence of numbers not in a.

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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

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

Crossrefs

Cf. A055562 (complement), A022424.

Programs

Magma

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

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 *)

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

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

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