cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A066645 a(n) = floor( (4/3)*Pi*n^3 ).

Original entry on oeis.org

0, 4, 33, 113, 268, 523, 904, 1436, 2144, 3053, 4188, 5575, 7238, 9202, 11494, 14137, 17157, 20579, 24429, 28730, 33510, 38792, 44602, 50965, 57905, 65449, 73622, 82447, 91952, 102160, 113097, 124788, 137258, 150532, 164636, 179594, 195432
Offset: 0

Views

Author

Amarnath Murthy, Dec 29 2001

Keywords

Comments

a(n) = A164086(A000578(n)). [Reinhard Zumkeller, Aug 11 2009]
Volume of a sphere of radius n, rounded down.

Links

Crossrefs

Cf. A000578, A135973, A164086.

Programs

  • Mathematica
    Table[ Floor[(4/3)Pi*n^3], {n, 0, 50} ]
  • Maxima
    A066645(n):=floor((4/3)*%pi*n^3)$
makelist(A066645(n),n,1,30); /* Martin Ettl, Nov 03 2012 */
  • PARI
    { for (n=0, 1000, write("b066645.txt", n, " ", floor((4/3)*Pi*n^3)) ) } \\ Harry J. Smith, Mar 16 2010
  • Sage
    n=100 # change n for more values
[floor(4/3*pi*r^3) for r in [0..n]] # Tom Edgar, Oct 10 2013

Formula

a(n) = floor((4/3)*Pi*n^3).
a(n) = A135973(n) - 1 for n > 0.

Extensions

More terms from Robert G. Wilson v, Jan 03 2002
0 prepended by T. D. Noe, Oct 10 2013

A109238 a(n) = floor(n*(e^2+1)/2).

Original entry on oeis.org

4, 8, 12, 16, 20, 25, 29, 33, 37, 41, 46, 50, 54, 58, 62, 67, 71, 75, 79, 83, 88, 92, 96, 100, 104, 109, 113, 117, 121, 125, 130, 134, 138, 142, 146, 151, 155, 159, 163, 167, 171, 176, 180, 184, 188, 192, 197, 201, 205, 209, 213, 218, 222, 226
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for (e^2+1)/2 = 4.19452...; complement of A109237.
From Reinhard Zumkeller, Aug 11 2009: (Start)
a(n) = A164086(n) for n <= 66;
a(n) = A109239(A109237(n)) and A109239(a(n)) = A109237(n). (End)

Links

Crossrefs

Cf. A109237, A109239, A164086.

Programs

  • Mathematica
    Floor[Range[60] (E^2+1)/2] (* Harvey P. Dale, Apr 10 2018 *)

Extensions

Typo in comment corrected by Reinhard Zumkeller, Aug 10 2009

A164087 Beatty sequence for 4*Pi/(4*Pi-3) = 1.3135986... .

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89, 90, 91, 93, 94
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 11 2009

Keywords

Comments

a(n) = A109237(n) for n <= 66;
complement of A164086;
a(n) = A164088(A164086(n)) and A164088(a(n)) = A164086(n).

Links

Crossrefs

Cf. A109237, A164086, A164088.

Programs

  • Mathematica
    Floor[4 Range[100]*Pi/(4*Pi - 3)] (* Wesley Ivan Hurt, Apr 25 2023 *)

Formula

a(n) = floor(4*n*Pi/(4*Pi-3)).

A164088 Self-inverse integer permutation induced by Beatty sequences for 4*Pi/3 and 4*Pi/(4*Pi-3).

Original entry on oeis.org

4, 8, 12, 1, 16, 20, 25, 2, 29, 33, 37, 3, 41, 46, 50, 5, 54, 58, 62, 6, 67, 71, 75, 79, 7, 83, 87, 92, 9, 96, 100, 104, 10, 108, 113, 117, 11, 121, 125, 129, 13, 134, 138, 142, 146, 14, 150, 154, 159, 15, 163, 167, 171, 17, 175, 180, 184, 18, 188, 192, 196, 19, 201, 205
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 11 2009

Keywords

Links

Crossrefs

Cf. A109239, A164086, A164087.

Formula

a(n) = A109239(n) for n <= 26;
a(A164086(n)) = A164087(n) and a(A164087(n)) = A164086(n).
Showing 1-4 of 4 results.

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