1,2

Let u(n), v(n) be defined by u(1)=v(1)=1, u(n+1)=u(n)+v(n), v(n+1)=u(n)v(n); then a(n)=u(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 01 2002

Consider the mapping f(a/b) = (a + b)/(ab). Taking a = 1 b = 1 to start with, and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/1, 2/1, 3/2, 5/6, 11/30, ... Sequence contains the numerators. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 24 2003

An infinite coprime sequence defined by recursion. - Michael Somos Mar 19 2004

D. Parisse, The Tower of Hanoi and the Stern-Brocot Array, Thesis, Munich, 1997.

Franklin T. Adams-Watters, Table of n, a(n) for n = 1..20

Index entries for sequences related to Stern's sequences

Index entries for sequences related to rooted trees

lim n -> infinity a(n)^PHI/A064847(n)=1 where PHI=(1+sqrt(5))/2 is the golden ratio. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 08 2002

Numerator of b(n) where b(n) = 1/numer(b(n-1)) + 1/denom(b(n-1)), b(1)=1.

a(n+1)=a(n)+a(1)a(2)...a(n-1). Also a(n+1)=a(n)+a(n-1)*(a(n)-a(n-1)), a(1)=1, a(2)=2.

(PARI) a(n)=local(an); if(n<1, 0, an=vector(max(2, n)); an[1]=1; an[2]=2; for(k=3, n, an[k]=an[k-1]-an[k-2]^2+an[k-1]*an[k-2]); an[n])

Cf. A001685, A064526, A064847.

Sequence in context: A111289 A127181 A113734 this_sequence A086506 A109462 A000905

Adjacent sequences: A003683 A003684 A003685 this_sequence A003687 A003688 A003689

nonn,easy,nice

Seva Lev (seva(AT)math.uga.edu)

Additional description from Andreas M. Hinz and Daniele Parisse (hinz(AT)appl-math.tu-muenchen.de).