login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Sum of first n terms of the simple continued fraction of Sum_{k>=0} 1/2^(2^k) (cf. A007400).
2

%I #10 Oct 13 2019 18:07:50

%S 0,1,5,7,11,15,21,25,27,31,37,39,43,49,53,57,59,63,69,71,75,79,85,89,

%T 91,97,101,103,107,113,117,121,123,127,133,135,139,143,149,153,155,

%U 159,165,167,171,177,181,185,187,193,197,199,203,207,213,217,219,225,229

%N Sum of first n terms of the simple continued fraction of Sum_{k>=0} 1/2^(2^k) (cf. A007400).

%F a(n) ~ 4n and a(n) < 4n.

%e The first 9 terms are 0, 1, 4, 2, 4, 4, 6, 4, 2, hence a(9)= 0 + 1 + 4 + 2 + 4 + 4 + 6 + 4 + 2 = 27.

%Y Cf. A007400.

%K easy,nonn

%O 1,3

%A _Benoit Cloitre_, Aug 18 2002