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

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)