OFFSET
1,3
COMMENTS
From Michel Dekking, Aug 26 2019: (Start)
This sequence is a generalized Beatty sequence. We know that A054770, the sequence of numbers whose Lucas representation includes L_0=2, is equal to A054770(n) = A000201(n) + 2*n - 1 = floor((phi+2)*n) - 1.
One also easily checks that the numbers 3-phi and phi+2 form a Beatty pair. This implies that the sequence with terms floor((3-phi)*n)-1 is the complement of A054770 in the natural numbers 0,1,2,...
It follows that a(n) = 3*n - floor(n*phi) - 2.
(End)
FORMULA
a(n) = floor((3-phi)*n)-1, where phi is the golden mean. - Michel Dekking, Aug 26 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Fred Lunnon, Aug 25 2001
STATUS
approved