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A065426 Incrementally larger terms in the continued fraction (A065645) for the twin prime constant (A005597). 0

%I #22 Aug 02 2023 18:14:15

%S 0,1,16,18,21,405,1199,2301,19965

%N Incrementally larger terms in the continued fraction (A065645) for the twin prime constant (A005597).

%H Gerhard Niklasch, <a href="https://people.mpim-bonn.mpg.de/moree/Moree-details.en.shtml">Some number-theoretical constants: 1000-digit values</a>

%t (* tpc copied from Niklasch reference *)

%t cof = ContinuedFraction[tpc, 969]; a = -1; k = 1; Do[ While[ cof[[k]] <= a, k++ ]; a = cof[[k]]; Print[a], {n, 1, 9} ]

%o (PARI) \\ Increasing lprec to 30000 gives no further term beyond 19965.

%o a065246(lprec) = {localprec(lprec); my (m=-1, T=prodeulerrat(1-1/(p-1)^2, 1, 3), c=contfrac(T)); for (k=1, #c, if (c[k]>m, print(c[k],", "); m=c[k]))};

%o a065246(1000) \\ _Hugo Pfoertner_, Aug 01 2023

%Y Cf. A005597 and A065645.

%K nonn,hard,more

%O 1,3

%A _Robert G. Wilson v_, Nov 15 2001

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