

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



