1,2

Also: a(1)=1, a(n)=maximal positive number <a(n-1) not encountered so far, if existing, else a(n)=4*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)=4*a(n-1).

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

a(n)=(11*4^(r/2)-5)/3-n, if both r and s are even, else a(n)=(23*4^((s-1)/2)-5)/3-n, where r=ceiling(2*log_4((3n+4)/7)) and s=ceiling(2*log_4((3n+4)/8)).

a(n)=(4^floor(1+(k+1)/2)+7*4^floor(k/2)-5)/3-n, where k=r, if r is odd, else k=s (with respect to r and s above; formally, k=((r+s)-(r-s)*(-1)^r)/2).

G.f.: g(x)=(x(1-2x)/(1-x)+4x^2*f'(x^(7/3))+(7/16)*(f'(x^(1/3))-4x-1))/(1-x) where f(x)=sum{k>=0, x^(4^k)} and f'(z)=derivative of f(x) at x=z.

a(n)=A133628(m)+A133628(m+1)+1-n, where m:=max{ k | A133628(k)<n }.

a(A133628(n)+1)=A133628(n+1).

a(A133628(n))=A133628(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=2 to p=10 see A132666 -132674.

Cf. A133628.

Adjacent sequences: A132665 A132666 A132667 this_sequence A132669 A132670 A132671

Sequence in context: A074066 A067016 A022295 this_sequence A018866 A021235 A020703

nonn

Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 24 2007, Sep 15 2007, Sep 23 2007