A065493 Decimal expansion of the Feller-Tornier constant (1 + A065474)/2.

6, 6, 1, 3, 1, 7, 0, 4, 9, 4, 6, 9, 6, 2, 2, 3, 3, 5, 2, 8, 9, 7, 6, 5, 8, 4, 6, 2, 7, 4, 1, 1, 8, 5, 3, 3, 2, 8, 5, 4, 7, 5, 2, 8, 9, 8, 3, 2, 9, 1, 6, 3, 5, 4, 9, 8, 0, 9, 0, 5, 6, 2, 6, 2, 2, 6, 6, 2, 5, 0, 3, 1, 7, 4, 3, 1, 2, 2, 3, 0, 4, 9, 4, 2, 2, 6, 1, 7, 4, 0, 7, 8, 4, 2, 8, 1, 8, 7

Offset

0,1

Comments

The asymptotic density of numbers with an even number of non-unitary prime divisors (A333634). - Amiram Eldar, May 23 2020

Named after the Croatian-American mathematician William Feller (1906-1970) and the German mathematician Erhard Tornier (1894-1982). - Amiram Eldar, Jun 16 2021

Links

Table of n, a(n) for n=0..97.

Jayadev S. Athreya, Cristian Cobeli, and Alexandru Zaharescu, Visibility phenomena in hypercubes, arXiv:2204.03147 [math.NT], 2022.

Willy Feller and Erhard Tornier, Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe, Mathematische Annalen, Vol. 107 (1933), pp. 188-232.

Mizan R. Khan and Riaz R. Khan, To count clean triangles we count on imph(n), arXiv:2012.11081 [math.CO], 2020. Mentions this constant.

G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]

Eric Weisstein's World of Mathematics, Feller-Tornier Constant.

Eric Weisstein's World of Mathematics, Prime Products.

Wikipedia, Feller-Tornier constant.

Example

0.661317049469622335289765846274...

Mathematica

digits = 98; r[n_] := -2^n; 1/2 + (1/2) Exp[NSum[r[n]*(PrimeZetaP[2*n]/n), {n, 1, Infinity}, NSumTerms -> 1000, WorkingPrecision -> 2 digits ]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 16 2016 *)

Prog

(PARI) (1 + prodeulerrat(1 - 2/p^2))/2 \\ Amiram Eldar, Mar 17 2021

Crossrefs

Cf. A065474, A078080, A333634.

Sequence in context: A176567 A372272 A283100 * A133890 A248059 A111719

Adjacent sequences: A065490 A065491 A065492 * A065494 A065495 A065496

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 19 2001

Status

approved