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Denominators of fractions converging to square root 3 satisfying: a(n)=1/a(n-1)+1/a(n-2)+ 1/a(n-3) or numerators of reciprocal satisfying: a(n)=1/(a(n-1)+ a(n-2)+ a(n-3)) with a(1,2,3)= 1
3

%I #9 Nov 03 2016 06:24:12

%S 1,1,1,1,3,21,777,267547,17878140297,16341834244642095861,

%T 478987257940772584908938949874389249,

%U 804559699103199797086217986081816861067730765554524831136628441253

%N Denominators of fractions converging to square root 3 satisfying: a(n)=1/a(n-1)+1/a(n-2)+ 1/a(n-3) or numerators of reciprocal satisfying: a(n)=1/(a(n-1)+ a(n-2)+ a(n-3)) with a(1,2,3)= 1

%C For other square roots of positive integers add or subtract more a(n) to formula and start off.

%H Harvey P. Dale, <a href="/A162924/b162924.txt">Table of n, a(n) for n = 1..16</a>

%e For n=5 a(5)= 1/1 + 1/1 + 1/3 = 7/3 (denominator) For n=5 a(5)= 1/(1 + 1 + 1/3) = 3/7 (numerator)

%t nxt[{a_,b_,c_}]:={b,c,1/a+1/b+1/c}; Denominator[Transpose[NestList[nxt,{1,1,1},15]][[1]]] (* _Harvey P. Dale_, Dec 09 2012 *)

%Y Cf. A162926 (numerators). A066932, A057677

%K nonn,frac

%O 1,5

%A _Mark Dols_, Jul 17 2009

%E More terms from _Harvey P. Dale_, Dec 09 2012