

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.


3



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
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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



