



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
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



MATHEMATICA

Table[2 Floor[n (1 + Sqrt[5])/2] + n  1, {n, 1, 100}] // Differences (* JeanFrançois Alcover, Dec 14 2018 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



