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A280135
Negative continued fraction of Pi (also called negative continued fraction expansion of Pi).
2
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.
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
KEYWORD
nonn
AUTHOR
Randy L. Ekl, Dec 26 2016
STATUS
approved