OFFSET
1,2
COMMENTS
Conjecture: 0 < n*r - a(n) < 1 for n >= 1, where r = (15 - sqrt(5))/10. It has been verified by computer that a(n) = floor(n*r) for n=1..3*10^6.
This conjecture can be proved from the result in the Comments of A287769, where it is shown that A287769 is a Sturmian sequence with slope s := 1 - 1/(3+phi) = (15+sqrt(5))/22. The conjecture then follows from Lemma 9.1.3 in "Automatic sequences", since r = 1/s. - Michel Dekking, Oct 11 2017
REFERENCES
Jean-Paul Allouche and Jeffrey Shallit, Automatic sequences, Theory, applications, generalizations, Cambridge University Press, Cambridge, 2003, xvi+571.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = floor(n*r), where r = (15 - sqrt(5))/10. - Michel Dekking, Oct 11 2017
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2017
STATUS
approved