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a(n) = floor(1/sin(x(n))) where x(n) is Pi truncated at the n-th decimal digit.
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%I #11 Aug 07 2023 08:00:11

%S 7,24,627,1687,10792,376847,1530011,18660269,278567575,1695509434,

%T 11136696004,102111268281,1260654956981,10725187563685,

%U 308788493220129,4193528956200935,25999253094360135,118166387818704584

%N a(n) = floor(1/sin(x(n))) where x(n) is Pi truncated at the n-th decimal digit.

%C a(n+1) = a(n) for n = 31, 49, 53, 64, 70, 76, 84, 96, 105, 115, 120, 127, ...

%F Is there a formula for lim m_{n -> oo} log(a(n))/n >= 2?

%e x(4)=3.1415 and 1/sin(x(4))=10792.889... hence a(4)=10792.

%o (PARI) a(n)=floor(1/sin(floor(Pi*10^n)/10^n))

%K nonn,base

%O 0,1

%A _Benoit Cloitre_, Sep 07 2002