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

1,1

Links

Table of n, a(n) for n=1..105.

Example

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.

Prog

(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}

Crossrefs

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

Sequence in context: A198873 A103987 A021359 * A153805 A011056 A201763

Adjacent sequences: A109168 A109169 A109170 * A109172 A109173 A109174

Keyword

nonn,cons

Author

Paul D. Hanna, Jun 21 2005

Status

approved