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 A162924 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
 1, 1, 1, 1, 3, 21, 777, 267547, 17878140297, 16341834244642095861, 478987257940772584908938949874389249, 804559699103199797086217986081816861067730765554524831136628441253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS For other square roots of positive integers add or subtract more a(n) to formula and start off. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..16 EXAMPLE 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) MATHEMATICA 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 *) CROSSREFS Cf. A162926 (numerators). A066932, A057677 Sequence in context: A291967 A171104 A057600 * A079269 A127104 A176430 Adjacent sequences: A162921 A162922 A162923 * A162925 A162926 A162927 KEYWORD nonn,frac AUTHOR Mark Dols, Jul 17 2009 EXTENSIONS More terms from Harvey P. Dale, Dec 09 2012 STATUS approved

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Last modified June 19 14:50 EDT 2024. Contains 373503 sequences. (Running on oeis4.)