1,2

Also: a(1)=1, a(n)=maximal positive number <a(n-1) not encountered so far, if existing, else a(n)=2*a(n-1).

Also: a(1)=1, a(n)=a(n-1)-1, if a(n-1)-1>0 and has not been encountered so far, else a(n)=2*a(n-1).

A reordering of the natural numbers. The sequence is self-inverse in that a(a(n))=n.

Almost certainly a duplicate of A132340. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 12 2008

G.f.: g(x)=(x(1-2x)/(1-x)+2x^2*f'(x^3)+3/4*(f'(x)-2x-1))/(1-x) where f(x)=sum{k>=0, x^(2^k)} and f'(z)=derivative of f(x) at x=z.

a(n)=5*2^(r/2)-3-n, if both r and s are even, else a(n)=7*2^((s-1)/2)-3-n, where r=ceiling(2*log_2((n+2)/3)) and s=ceiling(2*log_2((n+2)/2)-1).

a(n)=2^floor(1+(k+1)/2)+3*2^floor(k/2)-3-n, where k=r, if r is even, else k=s (with respect to r and s above; formally, k=((r+s)+(r-s)*(-1)^r)/2).

a(n)=A027383(m)+A027383(m+1)+1-n, where m:=max{ k | A027383(k)<n }.

a(A027383(n)+1)=A027383(n+1).

a(A027383(n))=A027383(n-1)+1 for n>0.

For formulae concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.

For p=3 to p=10 see A132667-132674.

For a similar recurrence rule concerning Fibonacci (A000045) and Lucas numbers (A000032) see A132664 and A132665.

Cf. A027383.

Sequence in context: A034701 A091857 A132340 this_sequence A116533 A087559 A091850

Adjacent sequences: A132663 A132664 A132665 this_sequence A132667 A132668 A132669

nonn,nice

Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 24 2007, Sep 15 2007