OFFSET
0,4
COMMENTS
a(n) + b(n) = n and as n -> +infinity, a(n) / b(n) converges to sqrt(3). For all n, a(n) / b(n) < sqrt(3).
FORMULA
a(1) = 0. b(n) = n - a(n). If (a(n) + 1) / b(n) < sqrt(3), then a(n+1) = a(n) + 1, else a(n+1) = a(n).
a(n) = floor(n*(3-sqrt(3))/2). - Vladeta Jovovic, Oct 04 2003
EXAMPLE
a(6)= 3 so b(6) = 6 - 3 = 3. a(7) = 4 because (a(6) + 1) / b(6) = 4/3 which is < sqrt(3). So b(7) = 7 - 4 = 3. a(8) = 5 because (a(7) + 1) / b(7) = 5/3 which is < sqrt(3).
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Robert A. Stump (bee_ess107(AT)msn.com), Sep 15 2002
STATUS
approved