1,2

Alternative descriptions (1): unique positive integer sequence taking values in {1,2} satisfying a(1)=1, a(2)=2 and a(a(1)+...+a(n))=a(n) for n >= 3.

(2) Start with 1,2; then for any k>=1, a(a(1)+...+a(k))=a(k), fill in any undefined terms by the rule that a(t) = 1 if a(t-1) = 2 and a(t) = 2 if a(t-1) = 1.

(3) a(1)= 1, a(2)=2, a(a(1)+a(2)+...+a(n))=a(n); a(a(1)+a(2)+...+a(n)+1)=3-a(n).

More generally, the sequence a(n)=floor(r*(n+2))-floor(r*(n+1)), r= (1/2) *(z+sqrt(z^2+4)), z integer >=1, is defined by a(1), a(2) and a(a(1)+a(2)+...+a(n)+f(z))=a(n); a(a(1)+a(2)+...+a(n)+f(z)+1)=(2z+1)-a(n) where f(1)=0, f(z)=z-2 for z>=2.

a(n) = A014675(n+1); sum(k = 1, n, a(k)) = A058065(n)

Apparently a(n) = A059426(n).

a(1)+a(2)=3 and a(a(1)+a(2)) must be a(2) so a(3)=2. Therefore a(a(1)+a(2)+a(3))=a(5)=2 and from the rule the "hole" a(4) is 1. Hence sequence begins 1,2,2,1,2,...

Rest@Nest[ Flatten[ # /. {1 -> 2, 2 -> {2, 1}}] &, {1}, 11] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 26 2006)

Same as A014675 without the first term.

Sequence in context: A144462 A112104 A059426 this_sequence A119469 A127439 A092788

Adjacent sequences: A082386 A082387 A082388 this_sequence A082390 A082391 A082392

nonn,nice,easy

Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 14 2003