A123170 Continued fraction for (sqrt(2) + 1/sqrt(2))*tanh(1/sqrt(2)).

1, 3, 2, 3, 21, 6, 33, 8, 1, 2, 4, 1, 2, 11, 57, 14, 69, 16, 1, 2, 8, 1, 2, 19, 93, 22, 105, 24, 1, 2, 12, 1, 2, 27, 129, 30, 141, 32, 1, 2, 16, 1, 2, 35, 165, 38, 177, 40, 1, 2, 20, 1, 2, 43, 201, 46, 213, 48, 1, 2, 24, 1, 2, 51, 237, 54, 249, 56, 1, 2, 28, 1, 2, 59, 273, 62, 285, 64

Offset

1,2

References

J. Borwein and D. Bailey, Mathematics by Experiment, Plausible Reasoning in the 21st Century, A. K. Peters, p. 77.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

For n > 1, a(10*n-9) = 4*n-4, a(10*n-8) = 1, a(10*n-7) = 2, a(10*n-4) = 8*n-5, a(10*n-5) = 36*n-15, a(10*n-4) = 8*n-2, a(10*n-3) = 36*n-3, a(10*n-2) = 8*n, a(10*n-1) = 1, a(10*n) = 2.

Empirical g.f.: x*(2*x^21 +x^20 -2*x^19 -x^18 +3*x^16 +2*x^15 +15*x^14 +5*x^13 -2*x^12 -5*x^11 +2*x^10 +2*x^9 +x^8 +8*x^7 +33*x^6 +6*x^5 +21*x^4 +3*x^3 +2*x^2 +3*x +1) / (x^20 -2*x^10 +1). - Colin Barker, Jun 28 2013

Mathematica

ContinuedFraction[3Tanh[1/Sqrt[2]]/Sqrt[2], 78] (* Benoit Cloitre, Oct 02 2006 *)

Prog

(Magma) SetDefaultRealField(RealField(220)); ContinuedFraction( (Sqrt(2)+1/Sqrt(2))*Tanh(1/Sqrt(2)) ); // G. C. Greubel, Jul 19 2023
(SageMath) continued_fraction_list((sqrt(2)+1/sqrt(2))*tanh(1/sqrt(2)), nterms=100) # G. C. Greubel, Jul 19 2023

Crossrefs

Sequence in context: A092950 A059239 A350517 * A253381 A091806 A248244

Adjacent sequences: A123167 A123168 A123169 * A123171 A123172 A123173

Keyword

nonn,cofr

Author

Benoit Cloitre, Oct 02 2006

Status

approved