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

1,2

Links

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

Example

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.

Prog

(PARI) {PQ(n)=if(n%2==1, (n+1)/2, 2*PQ(n/2))} {CFM=contfracpnqn(vector(500, n, PQ(n))); x=CFM[1, 1]/CFM[2, 1]*1.0}

Crossrefs

Cf. A109168 (continued fraction of x), A109170 (continued fraction of 2*x), A109171 (digits of 2*x).

Sequence in context: A021075 A232705 A245174 * A011291 A338670 A233590

Adjacent sequences: A109166 A109167 A109168 * A109170 A109171 A109172

Keyword

nonn,cons

Author

Paul D. Hanna, Jun 21 2005

Status

approved