A340153 Decimal expansion of Product_{p prime} (1 - 2/p^3).

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

Offset: 0

Author

Amiram Eldar, Dec 29 2020

Keywords

• nonn
• cons

Comments

The asymptotic density of the sequence of cubefree numbers k such that k+1 is also cubefree (A340152) (Carlitz, 1932).

Examples

			0.67689273700988199361023732672438921279767839745978...
		

Links

• Leonard Carlitz, On a problem in additive arithmetic (II), The Quarterly Journal of Mathematics, Vol. os-3, No. 1 (1932), pp. 273-290.

Crossrefs

Cf. A065474, A340152.

Programs

Mathematica

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

PARI

prodeulerrat(1 - 2/p^3)

Extensions

More digits from Vaclav Kotesovec, Jan 16 2021