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

1, 1, 1, 1, 3, 21, 777, 267547, 17878140297, 16341834244642095861, 478987257940772584908938949874389249, 804559699103199797086217986081816861067730765554524831136628441253

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