OFFSET
1,2
COMMENTS
The initial segments of signature sequences correspond to ranges of theta from a1/b1 to a2/b2 (including 1/0 as infinity); a/b appears as a bound, splitting two previous segments, at n = (a+1)(b+1)/2.
LINKS
Eric Weisstein's World of Mathematics, Signature Sequence
FORMULA
a(n) = 1 + sum( 2<=k<=n, A163822(k)).
EXAMPLE
For n = 6, the sequences and corresponding ranges for theta are:
1,1,1,1,1,1 0/1..1/5
1,1,1,1,1,2 1/5..1/4
1,1,1,1,2,1 1/4..1/3
1,1,1,2,1,2 1/3..1/2
1,1,2,1,2,1 1/2..2/3
1,1,2,1,2,3 2/3..1/1
1,2,1,3,2,1 1/1..3/2
1,2,1,3,2,4 3/2..2/1
1,2,3,1,4,2 2/1..3/1
1,2,3,4,1,5 3/1..4/1
1,2,3,4,5,1 4/1..5/1
1,2,3,4,5,6 5/1..1/0
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Aug 04 2009
STATUS
approved