A206256 Decimal expansion of Product_{p prime} (1 - 3/p^2).

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

Offset

0,2

Comments

For a randomly selected number k, this is the probability that k, k+1, k+2 all are squarefree.

Links

Table of n, a(n) for n=0..105.

Leon Mirsky, Note on an asymptotic formula connected with r-free integers, The Quarterly Journal of Mathematics, Vol. os-18, No. 1 (1947), pp. 178-182.

Leon Mirsky, Arithmetical pattern problems relating to divisibility by rth powers, Proceedings of the London Mathematical Society, Vol. s2-50, No. 1 (1949), pp. 497-508.

Example

0.1254869809058...

Maple

# See A175640 using efact := 1-3/p^2. - R. J. Mathar, Mar 22 2012

Mathematica

$MaxExtraPrecision = 500; m = 500; c = LinearRecurrence[{0, 3}, {0, -6}, m]; RealDigits[(1/4) * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n] - 1/2^n)/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]] (* Amiram Eldar, Oct 01 2019 *)

Prog

(PARI) prodeulerrat(1 - 3/p^2) \\ Amiram Eldar, Mar 16 2021

Crossrefs

Cf. A059956, A065474, A007675, A335131, A370600.

Sequence in context: A060710 A271853 A146101 * A093052 A081556 A187012

Adjacent sequences: A206253 A206254 A206255 * A206257 A206258 A206259

Keyword

nonn,cons

Author

N. J. A. Sloane, Feb 05 2012, based on a posting by Warren Smith to the Math Fun Mailing List, Feb 04 2012

Extensions

More terms from Amiram Eldar, Oct 01 2019

More terms from Vaclav Kotesovec, Dec 17 2019

Status

approved