A162926 Numerators of fractions converging to square root 3 satisfying: a(n)=1/a(n-1)+1/a(n-2)+ 1/a(n-3) or denominators of reciprocal satisfying: a(n)=1/(a(n-1)+ a(n-2)+ a(n-3)) with a(1,2,3)= 1

1, 1, 1, 3, 7, 37, 1033, 467757, 33820512481, 30277741778897513797, 785696122254571911501384128129833729, 1350037852944002174045556752948635277284099036085244331545069453543

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..12.

Example

For n=5 a(5)= 1/1 + 1/1 + 1/3 = 7/3 (numerator)
For n=5 a(5)= 1/(1 + 1 + 1/3) = 3/7 (denominator)
Convergents are 1, 1, 1, 3, 2.3333.., 1.7619047...., 1.748317..., 1.89172..., 1.852777..., 1.64032..., 1.677983... - R. J. Mathar, Nov 03 2016

Crossrefs

Cf. A162924 (denominators), A002194, A057677, A066932.

Sequence in context: A086031 A174734 A152560 * A042895 A173561 A258840

Adjacent sequences: A162923 A162924 A162925 * A162927 A162928 A162929

Keyword

nonn,frac

Author

Mark Dols, Jul 17 2009

Status

approved