cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A065426 #22 Aug 02 2023 18:14:15
%S A065426 0,1,16,18,21,405,1199,2301,19965
%N A065426 Incrementally larger terms in the continued fraction (A065645) for the twin prime constant (A005597).
%H A065426 Gerhard Niklasch, <a href="https://people.mpim-bonn.mpg.de/moree/Moree-details.en.shtml">Some number-theoretical constants: 1000-digit values</a>
%t A065426 (* tpc copied from Niklasch reference *)
%t A065426 cof = ContinuedFraction[tpc, 969]; a = -1; k = 1; Do[ While[ cof[[k]] <= a, k++ ]; a = cof[[k]]; Print[a], {n, 1, 9} ]
%o A065426 (PARI) \\ Increasing lprec to 30000 gives no further term beyond 19965.
%o A065426 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 A065426 a065246(1000) \\ _Hugo Pfoertner_, Aug 01 2023
%Y A065426 Cf. A005597 and A065645.
%K A065426 nonn,hard,more
%O A065426 1,3
%A A065426 _Robert G. Wilson v_, Nov 15 2001