

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
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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



