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A280136 Negative continued fraction of e (or negative continued fraction expansion of e). 1

%I

%S 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,

%T 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,

%U 2,2,2,3,24,3,2,2,2,2,2,2,2,2,2,2,2,2,2

%N Negative continued fraction of e (or negative continued fraction expansion of e).

%C 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.

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

%e e = 2.71828... = 3 - (1/(4 - (1/(3 - (1/(...))))).

%o (PARI) \p10000; p=exp(1.0); for(i=1, 300, print(i, " ", ceil(p)); p=ceil(p)-p; p=1/p )

%Y Cf. A003417 (continued fraction of e).

%Y Cf. A005131 (generalized continued fraction of e).

%Y Cf. A133570 (exact continued fraction of e).

%Y Cf. A228825 (delayed continued fraction of e).

%Y Cf. A280135 (negative continued fraction of Pi).

%K nonn

%O 1,1

%A _Randy L. Ekl_, Dec 26 2016

%E More terms from _Jinyuan Wang_, Mar 04 2020

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Last modified July 5 19:02 EDT 2020. Contains 335473 sequences. (Running on oeis4.)