A369094 Decimal expansion of the asymptotic probability that 2 random integer 3 X 3 matrices generate the ring M_3(Z).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Steven Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2022. See p. 40.

Rostyslav V. Kravchenko, Marcin Mazur, and Bogdan V. Petrenko, On the smallest number of generators and the probability of generating an algebra, Algebra & Number Theory, Vol. 6, No. 2 (2012), pp. 243-291; arXiv preprint, arXiv:1001.2873 [math.RA], 2010.

Formula

Equals 1/(zeta(2)^2*zeta(3)).

Example

0.30745246768036605163579854662211162944428861170079...

Mathematica

RealDigits[1/(Zeta[2]^2*Zeta[3]), 10, 120][[1]]

Prog

(PARI) 1/(zeta(2)^2*zeta(3))

Crossrefs

Cf. A002117, A013661, A369095.

Sequence in context: A098867 A062253 A290844 * A322018 A200339 A065419

Adjacent sequences: A369091 A369092 A369093 * A369095 A369096 A369097

Keyword

nonn,cons

Author

Amiram Eldar, Jan 13 2024

Status

approved