A242624 Decimal expansion of Product_{n>1} (1-1/n)^(1/n).

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

Offset: 0

Author

Jean-François Alcover, May 19 2014

Keywords

• nonn
• cons

Examples

			0.4545121805146463170328014636843273993...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9, pp. 121-122.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A085361, A242623, A244625, A245254.

Programs

Magma

SetDefaultRealField(RealField(100)); L:=RiemannZeta();  Exp((&+[(Evaluate(L,n)-1)/(1-n): n in [2..10^3]])); // G. C. Greubel, Nov 15 2018

Maple

evalf(exp(-sum((1-Zeta(n))/(1-n), n=2..infinity)), 120); # Vaclav Kotesovec, Dec 11 2015

Mathematica

Exp[-NSum[(1-Zeta[n])/(1-n), {n, 2, Infinity}, NSumTerms -> 300, WorkingPrecision -> 110]] // RealDigits[#, 10, 100]& // First

PARI

default(realprecision, 100); exp(suminf(n=2, (zeta(n)-1)/(1-n))) \\ G. C. Greubel, Nov 15 2018

Sage

numerical_approx(exp(sum((zeta(k)-1)/(1-k) for k in [2..1000])), digits=100) # G. C. Greubel, Nov 15 2018

Formula

From Amiram Eldar, Feb 06 2022: (Start)

Equals exp(-A085361).

Equals 1/A245254. (End)

Extensions

Mma modified and data extended by Jean-François Alcover, May 23 2014