%I A089961
%S A089961 3,4,7,3,11,3,3,18,3,5,5,3,29,3,4,9,3,8,4,3,47,3,4,6,3,14,3,3,13,3,6,4,
%T A089961 3,76,3,3,4,7,3,9,3,3,23,3,5,5,3,21,3,3,10,3,7,4,3,123
%N A089961 A sequence having both Fibonacci and Lucas numbers, in n = Lucas and 
               Fibonacci positions.
%C A089961 a(n) with n = Fibonacci numbers = corresponding Lucas numbers. a(n) with 
               n = Lucas numbers = corresponding Fibonacci numbers. Examples: a(8) 
               = 18, where 8 = F6 and 18 = L6. a(29) = 13, where 29 = L7 and 13 
               = F7.
%F A089961 1. a(n) = (A0899590(n) - 1). 2. a(n) = floor(1/({n*k}*(1 - {n*k})))- 
               1; where {x} = fractional part of x; k = phi^(-1).
%e A089961 1. a(5) = 11 = A089959(5) - 1.
%e A089961 2. a(5) = 11. Take 5*.6180339.. = 3.09169945...= x, then {x} = .090169945...; 
               with k = (3 - sqrt(5))/2 = .6180339...; Floor({n*k}*(1 - {n*k}) = 
               12. Then subtract 1, getting 11.
%Y A089961 Cf. A089959.
%Y A089961 Sequence in context: A130880 A026248 A082089 this_sequence A161775 A109823 
               A071051
%Y A089961 Adjacent sequences: A089958 A089959 A089960 this_sequence A089962 A089963 
               A089964
%K A089961 nonn,uned
%O A089961 1,1
%A A089961 Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 20 2003