The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319433 Take Zeckendorf representation of n (A014417(n)), drop least significant bit, take inverse Zeckendorf representation. 1
 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS In other words, the Zeckendorf representation of a(n) is obtained from the Zeckendorf representation of n by deleting the least significant bit. Theorem: The first differences (1,1,0,1,0,1,1,0,...) form the Fibonacci word A005614. (The proof is straightforward.) LINKS Rémy Sigrist, Table of n, a(n) for n = 2..25000 EXAMPLE n = 19 has Zeckendorf representation [1, 0, 1, 0, 0, 1], dropping last bit we get [1, 0, 1, 0, 0], which is the Zeckendorf representation of 11, so a(19) = 11. PROG (PARI) a(n) = my (f=2, v=0); while (fibonacci(f) < n, f++); while (n > 1, if (n >= fibonacci(f), v += fibonacci(f-1); n -= fibonacci(f); f--); f--); return (v) \\ Rémy Sigrist, Oct 04 2018 CROSSREFS Cf. A003714, A005614, A014417. Sequence in context: A103355 A029092 A280814 * A253671 A209081 A248610 Adjacent sequences:  A319430 A319431 A319432 * A319434 A319435 A319436 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 30 2018 EXTENSIONS More terms from Rémy Sigrist, Oct 04 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 22:24 EST 2020. Contains 338858 sequences. (Running on oeis4.)