cp's OEIS Frontend

A119811 Numerators of the convergents to the continued fraction for the constant A119809 defined by binary sums involving Beatty sequences: c = Sum_{n>=1} 1/2^A049472(n) = Sum_{n>=1} A001951(n)/2^n.

%I A119811 #3 Mar 30 2012 18:36:57
%S A119811 2,7,72,9511,1246930216,2742028548141904733479,
%T A119811 1737967067447512977484869808775151193351704374584616
%N A119811 Numerators of the convergents to the continued fraction for the constant A119809 defined by binary sums involving Beatty sequences: c = Sum_{n>=1} 1/2^A049472(n) = Sum_{n>=1} A001951(n)/2^n.
%C A119811 The number of digits in these numerators are (beginning at n=1): [1,1,2,4,10,22,52,124,297,717,1729,4173,10074,24319,58709,141735,..].
%e A119811 c = 2.32258852258806773012144068278798408011950250800432925665718...
%e A119811 Convergents begin:
%e A119811 [2/1, 7/3, 72/31, 9511/4095, 1246930216/536870911,...]
%e A119811 where the denominators of the convergents equal [2^A000129(n-1)-1]:
%e A119811 [1,3,31,4095,536870911,1180591620717411303423,...],
%e A119811 and A000129 is the Pell numbers.
%o A119811 (PARI) {a(n)=local(M=contfracpnqn(vector(n,k,if(k==1,2, 2^round(((1+sqrt(2))^(k-1)+(1-sqrt(2))^(k-1))/2) +2^round(((1+sqrt(2))^(k-2)-(1-sqrt(2))^(k-2))/(2*sqrt(2))))))); return(M[1,1])}
%Y A119811 Cf. A119809 (constant), A119811 (continued fraction), A000129; A119812 (dual constant).
%K A119811 frac,nonn
%O A119811 1,1
%A A119811 _Paul D. Hanna_, May 26 2006