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A280135 Negative continued fraction of Pi (also called negative continued fraction expansion of Pi). 1

%I

%S 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,

%T 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,

%U 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

%N Negative continued fraction of Pi (also called negative continued fraction expansion of Pi).

%C 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.

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

%e Pi = 4 - (1 / (2 - (1 / (2 - (1 / ...))))).

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

%Y Cf. A001203 (continued fraction of Pi).

%Y Cf. A133593 (exact continued fraction of Pi).

%Y Cf. A280136 (negative continued fraction of e).

%K nonn

%O 1,1

%A _Randy L. Ekl_, Dec 26 2016

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)