login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194584 Differences of A035336. 2
5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It appears that this is the Fibonacci word A003849, using 5's and 3's instead of 0's and 1's. In other words, {a(n)} is a fixed point of the morphism 5->53, 3->5.
Proof of this conjecture: since A035336(n) = (2*floor(n*phi) + n - 1) (with phi = (1+sqrt(5))/2) is a generalized Beatty sequence, this follows from Lemma 4 in Allouche and Dekking. - Michel Dekking, Oct 10 2018
Also differences of A089910. - Bob Selcoe, Sep 20 2014
Proof of this conjecture: this follows from the Carlitz-Scoville-Hoggatt theorem: compositions of the Wythoff A and B sequences are generalized Beatty sequences (cf. Theorem 1 in Allouche and Dekking). - Michel Dekking, Oct 10 2018
LINKS
J.-P. Allouche and F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424 [math.NT], 2018.
MATHEMATICA
Table[2 Floor[n (1 + Sqrt[5])/2] + n - 1, {n, 1, 100}] // Differences (* Jean-François Alcover, Dec 14 2018 *)
CROSSREFS
Sequence in context: A145439 A165096 A165098 * A073316 A245979 A277621
KEYWORD
nonn
AUTHOR
John W. Layman, Aug 29 2011
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 26 12:26 EST 2024. Contains 370352 sequences. (Running on oeis4.)