cp's OEIS Frontend

A109171 Decimal expansion of 2*x, where constant x (A109169) satisfies the condition that the continued fraction expansion of 2*x (A109170) is equal to the continued fraction expansion of x (A109168) interleaved with positive even numbers.

%I A109171 #10 Sep 09 2024 15:01:13
%S A109171 2,8,1,6,9,8,8,5,5,8,4,5,7,8,1,3,9,7,1,4,9,6,9,4,8,5,5,8,1,6,1,3,9,5,
%T A109171 9,8,3,2,2,7,9,9,7,9,1,1,5,6,4,1,0,2,5,6,2,9,3,2,5,2,7,6,3,5,0,4,9,7,
%U A109171 2,5,9,5,5,7,9,8,0,6,1,7,0,6,6,0,2,5,1,2,5,7,0,8,6,0,9,7,3,8,3,7,2,9,6,2,5
%N A109171 Decimal expansion of 2*x, where constant x (A109169) satisfies the condition that the continued fraction expansion of 2*x (A109170) is equal to the continued fraction expansion of x (A109168) interleaved with positive even numbers.
%e A109171 2*x=2.8169885584578139714969485581613959832279979115641025629325276350497259...
%e A109171 The continued fraction expansion of x = A109168:
%e A109171 [1; 2, 2, 4, 3, 4, 4, 8, 5, 6, 6, 8, 7, 8, 8, 16, ...];
%e A109171 the continued fraction expansion of 2*x = A109170:
%e A109171 [2;1, 4,2, 6,2, 8,4, 10,3, 12,4, 14,4, 16,8, 18,5, ...]
%e A109171 which equals the continued fraction of x interleaved with even numbers.
%o A109171 (PARI) {PQ(n)=if(n%2==1,(n+1)/2,2*PQ(n/2))}
%o A109171 {CFM=contfracpnqn(vector(500,n,PQ(n))); x2=CFM[1,1]/CFM[2,1]*2.0}
%Y A109171 Cf. A109168 (continued fraction of x), A109169 (digits of x), A109170 (continued fraction of 2*x).
%K A109171 nonn,cons
%O A109171 1,1
%A A109171 _Paul D. Hanna_, Jun 21 2005