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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(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 Table of n, a(n) for n=1..86. 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 Cf. A003849, A035336, A089910. Sequence in context: A145439 A165096 A165098 * A073316 A245979 A277621 Adjacent sequences: A194581 A194582 A194583 * A194585 A194586 A194587 KEYWORD nonn AUTHOR John W. Layman, Aug 29 2011 STATUS approved

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