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A165509
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Continued fraction expansion of sum of reciprocals of primorial numbers: 1/2 + 1/6 + 1/30 + 1/210 + ... .
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2
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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, 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, 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
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OFFSET
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0,3
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LINKS
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EXAMPLE
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0.705230171791800965147431682... = 0 + 1/(1 + 1/(2 + 1/(2 + 1/(1 + ...))))
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MATHEMATICA
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ContinuedFraction[Sum[1/Product[Prime[i], {i, n}], {n, 80}], 120] (* G. C. Greubel, Oct 21 2018 *)
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PROG
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(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])) }
(Magma) SetDefaultRealField(RealField(100)); ContinuedFraction( (&+[1/(&*[NthPrime(j):j in [1..n]]): n in [1..80]]) ); // G. C. Greubel, Oct 21 2018
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CROSSREFS
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KEYWORD
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cofr,nonn
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AUTHOR
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STATUS
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approved
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