A242623 -id:A242623 - cp's OEIS frontend

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

Jean-François Alcover, May 19 2014

			0.4545121805146463170328014636843273993...

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

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

Cf. A085361, A242623, A244625, A245254.

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

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

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

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

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

From Amiram Eldar, Feb 06 2022: (Start)
Equals exp(-A085361).
Equals 1/A245254. (End)

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

A244625 Decimal expansion of Product_{n>1} (1 - 1/n^2)^(1/n).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Jul 02 2014

			0.7993704013063328789872528539753525668777...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 Alladi-Grinstead Constant, p. 122.

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

Cf. A085361, A242623, A242624.

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

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

digits = 102; Exp[-NSum[(Zeta[2*n+1]-1)/n, {n, 1, Infinity}, NSumTerms -> 300, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First

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

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

Equals exp(-Sum_{n>0} (zeta(2*n+1) - 1)/n).
Equals A242623 * A242624.
Also equals A242623 * exp(-A085361).

A272028 Decimal expansion of Product_{p prime} (1+1/p)^(1/p), an infinite product considered and computed by Marc Deléglise.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Apr 18 2016

			1.46819112232299378107910175565555486192182334313301519669833294...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 p. 122.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A242623 (same product without restriction to primes).

digits = 98; Exp[NSum[(-1)^(n-1)*PrimeZetaP[n-1]/(n-2), {n, 3, Infinity}, WorkingPrecision -> digits+10, Method -> "AlternatingSigns"]] // RealDigits[#, 10, digits]& // First

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

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A244625 Decimal expansion of Product_{n>1} (1 - 1/n^2)^(1/n).

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Magma

Maple

Mathematica

PARI

Sage

Formula

A272028 Decimal expansion of Product_{p prime} (1+1/p)^(1/p), an infinite product considered and computed by Marc Deléglise.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica