0,4

Inverse of the Lucas sequence (A000032), nearly, since a(Lucas(n))=n except for n=1 (see A130241 and A130247 for other versions). For n>=2, a(n+1) is equal to the partial sum of the Lucas indicator sequence (see A102460).

a(n)=ceiling(log_phi((n+sqr(n^2-4))/2))=ceiling(arcosh(n/2)/ln(phi)) where phi=(1+sqr(5))/2.

a(n)=A130241(n-1)+1=A130245(n-1) for n>=3.

G.f.: g(x)=x/(1-x)*(2x^2+sum{k>=2, x^Lucas(k)}).

a(n)=ceiling(log_phi(n-1/2)) for n>=3, where phi is the golden ratio.

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

For partial sums see A130244. Other related sequences: A000032, A130241, A130245, A130247, A130250, A130256, A130260. Indicator sequence A102460. Fibonacci inverse see A130233 - A130240, A104162.

Sequence in context: A064004 A087827 A136528 this_sequence A130245 A087793 A030411

Adjacent sequences: A130239 A130240 A130241 this_sequence A130243 A130244 A130245

nonn

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