A099643 Continued fraction for Pi + 1/Pi.

3, 2, 5, 1, 2, 1, 3, 2, 1, 2, 1, 13, 897, 2, 8, 1, 2, 1, 1, 15, 2, 3, 2, 1, 1, 2, 1, 11, 2, 1117, 1, 12, 2, 1, 1, 2, 1, 18, 4, 187, 22, 1, 3, 3, 3, 14, 1, 2, 3, 1, 78, 3, 1, 1, 65, 3, 1, 4, 2, 2, 2, 1, 3, 16, 2, 5, 5, 2, 1, 4, 1, 3, 883, 1, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 15, 1, 2, 5, 1, 1, 2, 1, 9, 16, 1

Offset

0,1

Comments

Pi and 1/Pi have separately x and 1-shifted-x continued fraction coefficient series. This expansion apparently does not display connection with those of added terms.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Mathematica

ContinuedFraction[Pi+1/Pi, 128]

Prog

(PARI) contfrac(Pi + 1/Pi) \\ Amiram Eldar, Mar 08 2025

Crossrefs

Cf. A001203, A098801 (decimal expansion).

Sequence in context: A172216 A121490 A197293 * A224344 A113260 A378888

Adjacent sequences: A099640 A099641 A099642 * A099644 A099645 A099646

Keyword

cofr,nonn

Author

Labos Elemer, Nov 02 2004

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024

Status

approved