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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 = (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

Table of n, a(n) for n=1..86.

J.-P. Allouche, F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424 [math.NT], 2018.

CROSSREFS

Cf. A003849, A035336, A089910.

Sequence in context: A145439 A165096 A165098 * A073316 A245979 A277621

Adjacent sequences:  A194581 A194582 A194583 * A194585 A194586 A194587

KEYWORD

nonn,changed

AUTHOR

John W. Layman, Aug 29 2011

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)