A316389 Continued fraction expansion of largest root of x^3 - 7*x + 7.

1, 1, 2, 4, 20, 2, 3, 1, 6, 10, 5, 2, 2, 1, 2, 2, 1, 18, 1, 1, 3, 2, 1, 2, 1, 2, 1, 39, 2, 1, 1, 1, 13, 1, 2, 1, 30, 1, 1, 1, 3, 2, 5, 4, 1, 5, 1, 5, 1, 2, 1, 1, 94, 6, 2, 19, 11, 1, 60, 1, 1, 50, 2, 1, 1, 8, 53, 1, 3, 1, 6, 3, 2, 1, 5, 1, 1, 3, 4, 636, 1, 2, 1, 3, 3, 7, 9, 1, 2, 10, 3, 1, 22, 1, 119, 3, 32, 1, 2, 1

Offset

1,3

Comments

a(n) is identical to A039921(n-1) for n >= 3. The largest root of x^3 - 7*x + 7 equals (3*w-1)/(2*w-1) for w = 2*cos(Pi/7), where w is the number referenced in A039921. Interestingly enough, all three roots of x^3-7*x+7 have a continued fraction expansion that ends in 2, 3, 1, 6, 10, 5, 2, 2, 1, ... which is a(n) for n >= 5.

Links

Table of n, a(n) for n=1..100.

Example

1.69202147163009586962781489700206914019726...

Mathematica

ContinuedFraction[Root[x^3 - 7 x + 7, 3], 100]

Crossrefs

Cf. A039921.

Sequence in context: A063458 A332991 A132530 * A133521 A122158 A178223

Adjacent sequences: A316386 A316387 A316388 * A316390 A316391 A316392

Keyword

nonn,cofr

Author

Greg Dresden, Jul 01 2018

Status

approved