A359454 Decimal expansion of Knopfmacher's limit: Limit_{x -> 1 from below} (1/(1-x)) * Product_{k>=2} (1 - x^m(k)/(k+1)), where m(k) = A060681(k) = k - k/A020639(k).

2, 2, 9, 2, 1, 7, 3, 6, 9, 5, 3

Offset

1,1

Comments

The problem of calculating this limit was proposed by Knopfmacher (1999) and its value was calculated by Lichtblau (2000).

Links

Table of n, a(n) for n=1..11.

Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing, SIAM, Philadelphia, 2004. See Appendix D, Problem 3, p. 282.

Arnold Knopfmacher, A tricky limit, Usenet news group post to comp.soft-sys.math.mathematica, 1999.

Daniel Lichtblau, The evaluation of Knopfmacher's curious limit, Wolfram Research, Inc., Note of August 2000.

Daniel Lichtblau, Computing Knopfmacher's Limit, or My First Foray into Computational Mathematics, Reprise, Wolfram Research, Inc., 2009.

Example

2.2921736953...

Crossrefs

Cf. A020639, A060681.

Sequence in context: A274569 A082838 A074961 * A300450 A037289 A037290

Adjacent sequences: A359451 A359452 A359453 * A359455 A359456 A359457

Keyword

nonn,cons,more

Author

Amiram Eldar, Jan 02 2023

Status

approved