# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a022441 Showing 1-1 of 1 %I A022441 #45 Sep 08 2022 08:44:46 %S A022441 1,5,7,10,14,17,20,23,25,28,31,34,37,40,43,46,50,53,56,59,62,65,68,71, %T A022441 74,77,80,83,86,89,92,95,97,100,103,106,109,112,115,118,121,124,127, %U A022441 130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175,178 %N A022441 a(n) = c(n) + c(n-1) where c (A055562) is the sequence of numbers not in a. %H A022441 Ivan Neretin, Table of n, a(n) for n = 0..10000 %H A022441 J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264. %H A022441 R. Stephan, Some divide-and-conquer sequences ... %H A022441 R. Stephan, Table of generating functions %F A022441 a(n) + a(n-1) = 3n + 2 - (floor(log_2 n) mod 2) for n >= 1. - _Jeffrey Shallit_, Jun 08 2000 %F A022441 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 %F A022441 a(n) = A210770(2*n+1). - _Reinhard Zumkeller_, Mar 25 2012 %p A022441 A022441 := n-> `if`(n=0, 1, 3*n + 2 - (ilog2(n) mod 2)): %p A022441 seq(A022441(n), n= 0..59); %t A022441 Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2 + 1, #2 + 2}]]] &, {1, 5}, Range[58]] (* _Ivan Neretin_, Mar 30 2017 *) %t A022441 Table[If[n==0,1, 3*n+2 - Mod[Floor[Log[n]/Log[2]], 2]], {n,0,30}] (* _G. C. Greubel_, Mar 08 2018 *) %o A022441 (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 %o A022441 (Magma) [1] cat [3*n + 2 - (Floor((Log(n)/Log(2))) mod 2): n in [0..10]]; // _G. C. Greubel_, Mar 08 2018 %Y A022441 Cf. A055562 (complement), A022424. %K A022441 nonn,easy %O A022441 0,2 %A A022441 _Clark Kimberling_ %E A022441 More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 23 2000 %E A022441 Term a(16)=50 fixed by _Ivan Neretin_, Mar 30 2017 %E A022441 Updated by _Clark Kimberling_, Feb 19 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE