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A242624
Decimal expansion of Product_{n>1} (1-1/n)^(1/n).
6
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
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 p. 122.
LINKS
FORMULA
From Amiram Eldar, Feb 06 2022: (Start)
Equals exp(-A085361).
Equals 1/A245254. (End)
EXAMPLE
0.4545121805146463170328014636843273993...
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
PROG
(PARI) default(realprecision, 100); exp(suminf(n=2, (zeta(n)-1)/(1-n))) \\ G. C. Greubel, Nov 15 2018
(Magma) SetDefaultRealField(RealField(100)); L:=RiemannZeta(); Exp((&+[(Evaluate(L, n)-1)/(1-n): n in [2..10^3]])); // 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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Mma modified and data extended by Jean-François Alcover, May 23 2014
STATUS
approved