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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. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A233590 A078889

Adjacent sequences:  A109166 A109167 A109168 * A109170 A109171 A109172

KEYWORD

nonn,cons

AUTHOR

Paul D. Hanna, Jun 21 2005

STATUS

approved

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Last modified December 15 15:10 EST 2019. Contains 329999 sequences. (Running on oeis4.)