A048613 Number of terms (excluding the first) of A002211 for which the geometric mean produces progressively better approximations to Khinchin's constant (itself).

1, 2, 3, 15, 23, 26, 81, 104, 109, 111, 120, 127, 135, 136, 141, 142, 144, 145, 146, 147, 148, 5920, 5943, 8381, 8401, 89953, 91368, 267848, 353014

Offset

1,2

Comments

a(30) > 969679. - Hans Havermann, Jul 14 2024

Links

Table of n, a(n) for n=1..29.

Hans Havermann, Simple Continued Fraction Expansion of Khinchin's Constant.

Marek Wolf, Computer experiments with Mersenne primes, arXiv preprint arXiv:1112.2412 [math.NT], 2011.

Mathematica

cf=Rest[ContinuedFraction[Khinchin, 200]]; r=2; p=N[1, 50]; Do[p=p*cf[[i]]; m=Abs[p^(1/i)-Khinchin]; If[m<r, Print[i]; r=m], {i, Length[cf]}] (* Hans Havermann, Jul 16 2024 *)

Crossrefs

Cf. A002211, A209600.

Sequence in context: A347668 A325236 A037175 * A162890 A030072 A064219

Adjacent sequences: A048610 A048611 A048612 * A048614 A048615 A048616

Keyword

nice,nonn,more

Author

Hans Havermann

Extensions

a(28)-a(29) from Hans Havermann, Jul 14 2024

Status

approved