Search: id:A128273
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%I A128273
%S A128273 1,3,7,171,2401,419121,39647713,47740815747,30877916418391,
%T A128273 255080753983140651,1130395777976404261441,177322193432863810849593,
%U A128273 1944244855966235024678049078337,754657638581703992960984555289787011
%N A128273 a(n) = the denominator of b(n): {b(n)} is such that the continued fraction 
               (of rational terms) [b(1);b(2),...,b(n)] equals the F(n+1)^2/F(n)^2, 
               for every positive integer n, where F(n) is the n-th Fibonacci number.
%C A128273 limit{n -> inf} b(n)*b(n+1) = 1.
%H A128273 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A128273 b(n): 1, 1/3, 15/7, 77/171, 5301/2401,...
%e A128273 F(5)^2/F(4)^2 = 25/9 equals [b(1);b(2),b(3),b(4)] = 1 +1/(1/3 +1/(15/
               7 +171/77)).
%e A128273 F(6)^2/F(5)^2 = 64/25 equals [b(1);b(2),b(3),b(4),b(5)] = 1 +1/(1/3 +1/
               (15/7 +1/(77/171 +2401/5301)).
%p A128273 A128273 := proc(nmax) local a,b,i,n,ffrac ; b := [1] ; while nops(b) 
               < nmax do n := nops(b)+1 ; ffrac := (combinat[fibonacci](n+1)/combinat[fibonacci](n))^2 
               ; for i from 1 to n-1 do ffrac := 1/(ffrac-b[i]) ; od: b := [op(b),
               ffrac] ; od: a := [] ; for i from 1 to nops(b) do a := [op(a),denom(op(i,
               b))] ; od: RETURN(a) ; end: op(A128273(17)) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 08 2007
%Y A128273 Cf. A128272.
%Y A128273 Sequence in context: A119958 A031881 A114789 this_sequence A105763 A132564 
               A057619
%Y A128273 Adjacent sequences: A128270 A128271 A128272 this_sequence A128274 A128275 
               A128276
%K A128273 frac,nonn
%O A128273 1,2
%A A128273 Leroy Quet Feb 22 2007
%E A128273 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 08 2007

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