A109169 Decimal expansion of constant x such that the continued fraction expansion of 2*x (A109170) yields the continued fraction expansion of x (A109168) interleaved with positive even numbers.

1, 4, 0, 8, 4, 9, 4, 2, 7, 9, 2, 2, 8, 9, 0, 6, 9, 8, 5, 7, 4, 8, 4, 7, 4, 2, 7, 9, 0, 8, 0, 6, 9, 7, 9, 9, 1, 6, 1, 3, 9, 9, 8, 9, 5, 5, 7, 8, 2, 0, 5, 1, 2, 8, 1, 4, 6, 6, 2, 6, 3, 8, 1, 7, 5, 2, 4, 8, 6, 2, 9, 7, 7, 8, 9, 9, 0, 3, 0, 8, 5, 3, 3, 0, 1, 2, 5, 6, 2, 8, 5, 4, 3, 0, 4, 8, 6, 9, 1, 8, 6, 4, 8, 1, 2

Offset: 1

Author

Paul D. Hanna, Jun 21 2005

Keywords

• nonn
• cons

Examples

			x=1.408494279228906985748474279080697991613998955782051281466263817524862977...
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), A109170 (continued fraction of 2*x), A109171 (digits 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))); CFM[1,1]/CFM[2,1]*1.0}