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 1-3 of 3 results.

A109259 a(n) = floor(n*sqrt(2)^sqrt(2)).

Original entry on oeis.org

1, 3, 4, 6, 8, 9, 11, 13, 14, 16, 17, 19, 21, 22, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 79, 81, 83, 84, 86, 88, 89, 91, 93, 94, 96, 97, 99, 101, 102, 104
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for sqrt(2)^sqrt(2) = 1.63252...; complement of A109260.

Links

Crossrefs

Cf. A078333, A109261, A038127.

Programs

  • Magma
    [Floor(n*Sqrt(2)^Sqrt(2)): n in [1..100]]; // G. C. Greubel, Mar 27 2018
  • Mathematica
    With[{c=(Sqrt[2])^Sqrt[2]},Floor[c*Range[100]]] (* Harvey P. Dale, Mar 19 2018 *)
  • PARI
    for(n=1,100, print1(floor(n*sqrt(2)^sqrt(2)), ", ")) \\ G. C. Greubel, Mar 27 2018

A047480 Numbers that are congruent to {2, 5, 7} mod 8.

Original entry on oeis.org

2, 5, 7, 10, 13, 15, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 53, 55, 58, 61, 63, 66, 69, 71, 74, 77, 79, 82, 85, 87, 90, 93, 95, 98, 101, 103, 106, 109, 111, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 141, 143, 146, 149, 151, 154, 157, 159
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Different from A038127.
Cf. A047408.

Programs

  • Magma
    [n : n in [0..150] | n mod 8 in [2, 5, 7]]; // Wesley Ivan Hurt, Jun 10 2016
  • Maple
    A047480:=n->(24*n-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047480(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
  • Mathematica
    Select[Range[0, 150], MemberQ[{2, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
Flatten[Table[8 n + {2, 5, 7}, {n, 0, 150}]] (* Vincenzo Librandi, Jun 12 2016 *)
LinearRecurrence[{1,0,1,-1},{2,5,7,10},100] (* Harvey P. Dale, Jun 18 2018 *)

Formula

G.f.: x*(1+x)*(x^2+x+2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (24*n-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-6. (End)
a(n) = A047408(n) + 1. - Lorenzo Sauras Altuzarra, Jan 31 2023

A064724 A Beatty sequence for 2^sqrt(2).

Original entry on oeis.org

1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 20, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 38, 40, 41, 43, 44, 46, 48, 49, 51, 52, 54, 56, 57, 59, 60, 62, 64, 65, 67, 68, 70, 72, 73, 75, 76, 78, 80, 81, 83, 84, 86, 88, 89, 91, 92, 94, 96, 97, 99, 100, 102, 104, 105, 107, 108, 110
Offset: 1

Views

Author

Robert G. Wilson v, Oct 16 2001

Keywords

Links

Crossrefs

Beatty complement is A038127.
Note that this sequence differs from A047416, 589 is in this sequence while 588 is in A047416.

Programs

  • Magma
    [Floor(n*2^Sqrt(2)/(2^Sqrt(2) - 1)): n in [1..100]]; // G. C. Greubel, Sep 09 2018
  • Mathematica
    Table[Floor[n*(2^Sqrt[2])/(2^Sqrt[2] - 1)], {n, 1, 70} ]
  • PARI
    { default(realprecision, 100); b=2^sqrt(2); b=b/(b - 1); for (n = 1, 2000, write("b064724.txt", n, " ", floor(n*b)) ) } \\ Harry J. Smith, Sep 23 2009
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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