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A280136
Negative continued fraction of e (or negative continued fraction expansion of e).
2
3, 4, 3, 2, 2, 2, 3, 8, 3, 2, 2, 2, 2, 2, 2, 2, 3, 12, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 16, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 20, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 24, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
OFFSET
1,1
COMMENTS
After the first term (3), a pattern of groups consisting, for m>=1, of the number 4m, followed by 3, then 4m-1 2's, then 3.
REFERENCES
Leonard Eugene Dickson, History of the Theory of Numbers, page 379.
EXAMPLE
e = 2.71828... = 3 - (1/(4 - (1/(3 - (1/(...))))).
PROG
(PARI) \p10000; p=exp(1.0); for(i=1, 300, print(i, " ", ceil(p)); p=ceil(p)-p; p=1/p )
CROSSREFS
Cf. A003417 (continued fraction of e).
Cf. A005131 (generalized continued fraction of e).
Cf. A133570 (exact continued fraction of e).
Cf. A228825 (delayed continued fraction of e).
Cf. A280135 (negative continued fraction of Pi).
Sequence in context: A225445 A167877 A308430 * A258451 A332412 A333229
KEYWORD
nonn
AUTHOR
Randy L. Ekl, Dec 26 2016
EXTENSIONS
More terms from Jinyuan Wang, Mar 04 2020
STATUS
approved