A088435 - OEIS

%I #13 Aug 12 2017 13:02:49

%S 3,2,2,1,2,3,2,1,3,2,1,2,2,3,2,1,3,2,2,1,2,3,1,2,3,2,1,2,2,3,2,1,3,2,

%T 2,1,2,3,2,1,3,2,1,2,2,3,1,2,3,2,2,1,2,3,1,2,3,2,1,2,2,3,2,1,3,2,2,1,

%U 2,3,2,1,3,2,1,2,2,3,2,1,3,2,2,1,2,3,1,2,3,2,1,2,2,3,1,2,3,2,2,1,2,3,2,1,3

%N 1/2 + half of the (n+1)-st component of the continued fraction expansion of sum(k>=1,1/3^(2^k)).

%C To construct the sequence use the rule : a(1)=3, then a(a(1)+a(2)+...+a(n)+1)=2+(-1)^n and fill in any undefined place with 2.

%H Antti Karttunen, <a href="/A088435/b088435.txt">Table of n, a(n) for n = 1..8192</a> (computed from the b-file of A004200 provided by _Harry J. Smith_)

%F a(n) = (1/2) * (1+A004200(n+1)).

%F a(a(1)+a(2)+...+a(n)+1) = 2+(-1)^n.

%e Example to illustrate the comment : a(a(1)+1) = a(4) = 2+(-1)^1 = 1 and a(2), a(3) are undefined. The rule forces a(2) = a(3) = 2.

%Y Cf. A088431.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Nov 08 2003