A002432 -id:A002432 - cp's OEIS frontend

A114474 Number of decimal digits in the denominator of Zeta(10^n).

1, 5, 133, 2277, 32660, 426486, 5264705, 62646781

Offset: 0

Eric W. Weisstein, Dec 01 2005

J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function

Table[ Floor[ Log[ 10, Denominator[ Zeta[ 10^n]]] + 1], {n, 0, 6}] (* Robert G. Wilson v, Dec 01 2005 *)
IntegerLength[Denominator[Zeta[10^Range[0,7]]]] (* Harvey P. Dale, Aug 18 2016 *)

a(7) from Vaclav Kotesovec, Mar 05 2016

A188060 Numerator of 8^(2n-1) |B(2n)| / (2n)!, where B() are the Bernoulli numbers.

Original entry on oeis.org

8, 128, 4096, 32768, 1048576, 11593056256, 536870912, 7767448354816, 3014517285978112, 191986824837595136, 2733227576976736256, 66530577009460375453696, 5926115612870995607552, 488951148984934932554973184, 7946710949908368748447692488704, 71105936114697022329949662478336

Offset: 1

Eric Desbiaux, Apr 15 2011

nonn

Start with zeta(2n) = (2Pi)^(2n) |B(2n)| /(2 (2n)!) and replace Pi by 4 arctan(1) and take the numerator of the rational part. The denominator is given by A036278.

			8/3,128/45,4096/945,32768/4725,...

Cf. A002432, A046988, A036278.

 f:=n->8^(2*n)*abs(B(2*n))/(2*(2*n)!); [seq(numer(f(n)),n=1..60)];

Entry revised by N. J. A. Sloane, Apr 17 2011

A309946 a(n) = floor(Pi^n/Zeta(n)).

Original entry on oeis.org

0, 6, 25, 90, 295, 945, 2995, 9450, 29749, 93555, 294058, 924041, 2903320, 9121612, 28657269, 90030844, 282842403, 888579011, 2791558622, 8769948429, 27551618702, 86555983552, 271923674474, 854273468992, 2683779334331, 8431341566236, 26487840921750, 83214006759229, 261424512797515

Offset: 1

Seiichi Manyama, Aug 24 2019

nonn

			Pi^12/Zeta(12) = 638512875/691 = 924041.78... So a(12) = 924041.

Index entries for zeta function.

Decimal expansion of Pi^k/Zeta(k): A308637 (k = 3), A309926 (k = 5), A309927 (k = 7), A309928 (k = 9), A309929 (k = 11).

Cf. A001672 (floor(Pi^n)), A002432, A046988, A100594.

Table[Floor[Pi^n/Zeta[n]], {n, 20}] (* Alonso del Arte, Aug 24 2019 *)

{a(n) = if(n==1, 0, n==4, 90, floor(Pi^n/zeta(n)))}

a(2*n) = A100594(n).

A340243 a(n) = denominator((2n-1)zeta(2n)/Pi^(2n)).

Original entry on oeis.org

2, 6, 30, 189, 1350, 10395, 58046625, 1403325, 21709437750, 2292899734125, 80596287646875, 640374140030625, 8779111824511153125, 443779279041223125, 20913098524817639765625, 195202717402382161174828125, 2015813566807172297008593750, 367589532770719654160390625

Offset: 0

Artur Jasinski, Jan 01 2021

For numerators a(n+1) see A046988.

			1/2, 1/6, 1/30, 1/189, 1/1350, 1/10395, 691/58046625, 2/1403325, 3617/21709437750, 43867/2292899734125, ...

Cf. A002432, A027642, A046988, A176289, A164555.

a := n -> denom((2*n-1)*Zeta(2*n)/Pi^(2*n));
seq(a(n), n=0..17); # Peter Luschny, Jan 12 2021

Denominator[Table[(2 n - 1)*Zeta[2 n]/Pi^(2 n), {n, 0, 16}]]

a(n) = denominator((2*n-1)*2^(2*n-1)*bernfrac(2*n)/(2*n)!); \\ Michel Marcus, Jun 15 2022

a(n) = denominator((2*n-1)*2^(2*n-1)*Bernoulli(2*n)/(2*n)!). - Peter Luschny, Jan 12 2021

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A114474 Number of decimal digits in the denominator of Zeta(10^n).

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A188060 Numerator of 8^(2n-1) |B(2n)| / (2n)!, where B() are the Bernoulli numbers.

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A309946 a(n) = floor(Pi^n/Zeta(n)).

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A340243 a(n) = denominator((2*n-1)*zeta(2*n)/Pi^(2*n)).

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A340243 a(n) = denominator((2n-1)zeta(2n)/Pi^(2n)).