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

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.4.1, p. 106.

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