A309926 -id:A309926 - cp's OEIS frontend

A308637 Decimal expansion of Pi^3/Zeta(3).

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

Offset: 2

Seiichi Manyama, Aug 23 2019

Index entries for zeta function.

-----+---------------------------------
   n |  Zeta(n)
-----+---------------------------------
   2 |     Pi^2  / 6         = A013661.
   3 |     Pi^3  / 25.79...  = A002117.
   4 |     Pi^4  / 90        = A013662.
   5 |     Pi^5  / A309926   = A013663.
   6 |     Pi^6  / 945       = A013664.
   7 |     Pi^7  / A309927   = A013665.
   8 |     Pi^8  / 9450      = A013666.
   9 |     Pi^9  / A309928   = A013667.
  10 |     Pi^10 / 93555     = A013668.
  11 |     Pi^11 / A309929   = A013669.
  12 | 691*Pi^12 / 638512875 = A013670.
...
Cf. A002432, A091925, A276120 (Zeta(3)/Pi^3).

RealDigits[Pi^3/Zeta[3], 10, 100][[1]] (* Amiram Eldar, Aug 24 2019 *)

PARI
```
Pi^3/zeta(3)
```

Pi^3/Zeta(3) = A091925/A002117.

More terms from Amiram Eldar, Aug 24 2019

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).

cp's OEIS Frontend

A308637 Decimal expansion of Pi^3/Zeta(3).

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