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A280135 Negative continued fraction of Pi (also called negative continued fraction expansion of Pi). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A303577 A010314

Adjacent sequences:  A280132 A280133 A280134 * A280136 A280137 A280138

KEYWORD

nonn

AUTHOR

Randy L. Ekl, Dec 26 2016

STATUS

approved

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Last modified March 28 07:45 EDT 2020. Contains 333079 sequences. (Running on oeis4.)