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A162924
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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
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3
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1, 1, 1, 1, 3, 21, 777, 267547, 17878140297, 16341834244642095861, 478987257940772584908938949874389249, 804559699103199797086217986081816861067730765554524831136628441253
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OFFSET
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1,5
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COMMENTS
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For other square roots of positive integers add or subtract more a(n) to formula and start off.
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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