The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 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. 2
 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.) The difference sequence agrees with A005614 after the first two terms of A005614. - Clark Kimberling, Dec 29 2020 LINKS Rémy Sigrist, Table of n, a(n) for n = 2..25000 FORMULA a(n) = floor((n+2)/tau)-1, where tau = golden ratio. - Clark Kimberling, Dec 29 2020; corrected by Harry Altman, Jun 06 2024 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. MATHEMATICA r = (1 + Sqrt[5])/2; t = Table[Floor[(n - 1)/r] + 2, {n, 0, 150}] (* A319433 *) Differences[t] (* A005614 after the 1st 2 terms *) (* Clark Kimberling, Dec 29 2020 *) 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: A347707 A029092 A280814 * A253671 A209081 A248610 Adjacent sequences: A319430 A319431 A319432 * A319434 A319435 A319436 KEYWORD nonn,base,changed 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 02:19 EDT 2024. Contains 373416 sequences. (Running on oeis4.)