A280135 Negative continued fraction of Pi (also called negative continued fraction expansion of Pi).

4, 2, 2, 2, 2, 2, 2, 17, 294, 3, 4, 5, 16, 2, 3, 4, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,1

Comments

Appears that these terms are related to continued fraction of Pi through simple transforms; original continued fraction terms X,1 -> negative continued fraction term X+2 (e.g., 15,1->17, and 292,1->294); other transforms are to be determined.

References

Leonard Eugene Dickson, History of the Theory of Numbers, page 379.

Links

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

Example

Pi = 4 - (1 / (2 - (1 / (2 - (1 / ...))))).

Prog

(PARI)  \p10000; p=Pi; for(i=1, 300, print(i, " ", ceil(p)); p=ceil(p)-p; p=1/p )

Crossrefs

Cf. A001203 (continued fraction of Pi).

Cf. A133593 (exact continued fraction of Pi).

Cf. A280136 (negative continued fraction of e).

Sequence in context: A254969 A137239 A136714 * A297825 A338150 A303577

Adjacent sequences: A280132 A280133 A280134 * A280136 A280137 A280138

Keyword

nonn

Author

Randy L. Ekl, Dec 26 2016

Status

approved