1,3

Inverse of the Lucas sequence (A000032), nearly, since a(Lucas(n))=n for n>=1 (see A130242 and A130247 for other versions). For n>=2, a(n)+1 is equal to the partial sum of the Lucas indicator sequence (see A102460). Identical to A130247 except for n=2.

a(n)=floor(log_phi((n+sqr(n^2+4))/2))=floor(arsinh(n/2)/ln(phi)) where phi=(1+sqr(5))/2.

a(n)=A130242(n+1)-1 for n>=2. a(n)=A130247(n) except for n=2.

G.f.: g(x)=1/(1-x)*sum{k>=1, x^Lucas(k)}.

a(n)=floor(log_phi(n+1/2)) for n>=2, where phi is the golden ratio.

a(10)=4, since Lucas(4)=7<=10 but Lucas(5)=11>10.

For partial sums see A130243. Other related sequences: A000032, A130242, A130245, A130247, A130249, A130255, A130259. Indicator sequence A102460. Fibonacci inverse see A130233 - A130240, A104162.

Sequence in context: A103586 A117806 A085423 this_sequence A130247 A087839 A106742

Adjacent sequences: A130238 A130239 A130240 this_sequence A130242 A130243 A130244

nonn

Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 19 2007, Jul 02 2007