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A081478 Consider the mapping f(a/b) = (a - b)/(ab). Taking a = 2 b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 2/1,1/2,-1/2,-3/-2,-1/6,... Sequence contains the denominators. 2
1, 2, 2, -2, 6, -6, 42, -42, 1806, -1806, 3263442, -3263442, 10650056950806, -10650056950806, 113423713055421844361000442, -113423713055421844361000442, 12864938683278671740537145998360961546653259485195806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The mapping f(a/b) = (a + b)/(a - b). Taking a = 2 b = 1 to start with and carrying out this mapping repeatedly on each new (reduced)rational number gives the periodic sequence 2/1,3/1,2/1,3/1,...

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..26

MATHEMATICA

Last /@ NestList[{(#1 - #2), #1 #2} & @@ # &, {2, 1}, 16] (* Michael De Vlieger, Sep 04 2016 *)

PROG

(Sage)

# Variant with first four terms slightly different. Absolute values.

def A081478_abs():

    x, y = 1, 2

    yield x

    while true:

       yield x

       x, y = x * y, x//y + 1

a = A081478_abs(); print [a.next() for i in range(17)]  # Peter Luschny, Dec 17 2015

CROSSREFS

A003687 gives the numerators.

Cf. A007018.

Sequence in context: A139552 A292140 A064943 * A105341 A194676 A151694

Adjacent sequences:  A081475 A081476 A081477 * A081479 A081480 A081481

KEYWORD

sign,frac

AUTHOR

Amarnath Murthy, Mar 24 2003

EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

STATUS

approved

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)