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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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)