



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
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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 fixedpoint 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 CarlitzScovilleHoggatt 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.


MATHEMATICA

Table[2 Floor[n (1 + Sqrt[5])/2] + n  1, {n, 1, 100}] // Differences (* JeanFrançois 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



