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

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

Offset: 1

Author

Robert G. Wilson v, Nov 15 2001

Keywords

• nonn
• hard
• more

Links

• Gerhard Niklasch, Some number-theoretical constants: 1000-digit values

Crossrefs

Cf. A005597 and A065645.

Programs

Mathematica

(* tpc copied from Niklasch reference *)
cof = ContinuedFraction[tpc, 969]; a = -1; k = 1; Do[ While[ cof[[k]] <= a, k++ ]; a = cof[[k]]; Print[a], {n, 1, 9} ]

PARI

\\ Increasing lprec to 30000 gives no further term beyond 19965.
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]))};
a065246(1000) \\ Hugo Pfoertner, Aug 01 2023