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A165509 Continued fraction expansion of sum of reciprocals of primorial numbers: 1/2 + 1/6 + 1/30 + 1/210 + ... .

%I A165509 #27 Sep 08 2022 08:45:47
%S A165509 0,1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,5,8,1,1,5,1,22,1,1,1,2,2,
%T A165509 1,1,46,1,1,4,1,53,1,3,2,1,3,1,2,1,2,2,8,11,1,7,1,28,1,3,1,2,2,4,7,16,
%U A165509 5,1,1,2,1,2,1,1,2,1,5,3,17,1,7,2,3,66,1,1,4,1,27,12,2,1,1,3,9,1,12,14,2,4
%N A165509 Continued fraction expansion of sum of reciprocals of primorial numbers: 1/2 + 1/6 + 1/30 + 1/210 + ... .
%H A165509 Harry J. Smith, <a href="/A165509/b165509.txt">Table of n, a(n) for n = 0..20000</a>
%e A165509 0.705230171791800965147431682... = 0 + 1/(1 + 1/(2 + 1/(2 + 1/(1 + ...))))
%t A165509 ContinuedFraction[Sum[1/Product[Prime[i], {i, n}], {n, 80}], 120] (* _G. C. Greubel_, Oct 21 2018 *)
%o A165509 (PARI) { allocatemem(932245000); default(realprecision, 21000); p=1; s=x=0; for (k=1, 10^9, p*=prime(k); s+=1.0/p; if (s==x, break); x=s ); x=contfrac(s); for (n=0, 20000, write("b165509.txt", n, " ", x[n+1])) }
%o A165509 (Magma) SetDefaultRealField(RealField(100)); ContinuedFraction( (&+[1/(&*[NthPrime(j):j in [1..n]]): n in [1..80]]) ); // _G. C. Greubel_, Oct 21 2018
%Y A165509 Cf. A064648 (decimal expansion).
%K A165509 cofr,nonn
%O A165509 0,3
%A A165509 _Harry J. Smith_, Sep 21 2009