A081478 - OEIS

A081478

Consider the mapping f(a/b) = (a - b)/(ab). Taking a = 2 and 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.

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 and 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

FORMULA

a(2n-1) = A007018(n-1), a(2n) = -A007018(n-1) for n >= 2. - Jianing Song, Oct 10 2021

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