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A109170 Continued fraction expansion of 2*x which equals the continued fraction of x (A109168) interleaved with positive even numbers. 4
2, 1, 4, 2, 6, 2, 8, 4, 10, 3, 12, 4, 14, 4, 16, 8, 18, 5, 20, 6, 22, 6, 24, 8, 26, 7, 28, 8, 30, 8, 32, 16, 34, 9, 36, 10, 38, 10, 40, 12, 42, 11, 44, 12, 46, 12, 48, 16, 50, 13, 52, 14, 54, 14, 56, 16, 58, 15, 60, 16, 62, 16, 64, 32, 66, 17, 68, 18, 70, 18, 72, 20, 74, 19, 76, 20, 78 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..77.

FORMULA

For n>=1: a(2*n-1) = 2*n, a(4*n-2) = n, a(4*n) = 2*a(2*n).

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) a(n)=if(n%2==1, (n+1), if(n%4==2, (n+2)/4, 2*a(n/2)))

CROSSREFS

Cf. A109168 (continued fraction of x), A109169 (digits of x), A109171 (digits of 2*x).

Sequence in context: A093819 A089929 A131888 * A225368 A099311 A349442

Adjacent sequences:  A109167 A109168 A109169 * A109171 A109172 A109173

KEYWORD

cofr,nonn

AUTHOR

Paul D. Hanna, Jun 21 2005

STATUS

approved

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Last modified December 2 10:53 EST 2021. Contains 349440 sequences. (Running on oeis4.)