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.

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, 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, 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

Offset: 1

Author

Paul D. Hanna, Jun 21 2005

Keywords

• nonn
• cons

Examples

			2*x=2.8169885584578139714969485581613959832279979115641025629325276350497259...
The continued fraction expansion of x = A109168:
[1; 2, 2, 4, 3, 4, 4, 8, 5, 6, 6, 8, 7, 8, 8, 16, ...];
the continued fraction expansion of 2*x = A109170:
[2;1, 4,2, 6,2, 8,4, 10,3, 12,4, 14,4, 16,8, 18,5, ...]
which equals the continued fraction of x interleaved with even numbers.
		

Crossrefs

Cf. A109168 (continued fraction of x), A109169 (digits of x), A109170 (continued fraction of 2*x).

Programs

PARI

{PQ(n)=if(n%2==1,(n+1)/2,2*PQ(n/2))}
{CFM=contfracpnqn(vector(500,n,PQ(n))); x2=CFM[1,1]/CFM[2,1]*2.0}