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.

A184909 a(n) = n + floor(n*s/r) + floor(n*t/r), where r=2^(1/5), s=r^2, t=r^3.

Original entry on oeis.org

3, 6, 9, 13, 16, 19, 24, 27, 30, 34, 37, 40, 44, 48, 51, 55, 58, 61, 65, 68, 72, 76, 79, 82, 85, 89, 93, 96, 100, 103, 106, 110, 113, 117, 121, 124, 127, 131, 134, 137, 142, 145, 148, 152, 155, 158, 162, 166, 169, 172, 176, 179, 182, 187, 190, 193, 197, 200, 203, 207
Offset: 1

Views

Author

Clark Kimberling, Jan 25 2011

Keywords

Crossrefs

Cf. A005531, A005533, A011093.
Cf. A184910, A184911, A378142, A378185, A379510.

Programs

  • Mathematica
    r = 2^(1/5); s = r^2; t = r^3;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 120}]  (* A184909 *)
Table[b[n], {n, 1, 120}]  (* A184910 *)
Table[c[n], {n, 1, 120}]  (* A184911 *)
(* Clark Kimberling, Jan 18 2025 *)

Extensions

Definition in name corrected by Clark Kimberling, Jan 18 2025

A003118 Continued fraction for fifth root of 4.

Original entry on oeis.org

1, 3, 7, 1, 2, 2, 1, 2, 4, 56, 1, 14, 2, 1, 1, 3, 5, 6, 2, 1, 1, 2, 1, 1, 8, 1, 2, 2, 1, 5, 1, 4, 1, 1, 3, 3, 1, 1, 3, 7, 4, 1, 10, 1, 2, 1, 8, 2, 4, 1, 1, 9, 2, 2, 2, 1, 2, 1, 1, 1, 92, 1, 26, 4, 31, 1, 2, 4, 1, 62, 8, 5, 1, 1, 1, 2, 1, 1, 63, 1, 2, 5, 4, 2, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			1.319507910772894259374001971... = 1 + 1/(3 + 1/(7 + 1/(1 + 1/(2 + ...)))). - _Harry J. Smith_, May 11 2009

References

  • H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005533 (decimal expansion).

Programs

  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(4^(1/5)); for (n=1, 20000, write("b003118.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 11 2009

Extensions

Offset changed by Andrew Howroyd, Jul 05 2024

A018123 Powers of fifth root of 4 rounded down.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 5, 6, 9, 12, 16, 21, 27, 36, 48, 64, 84, 111, 147, 194, 256, 337, 445, 588, 776, 1024, 1351, 1782, 2352, 3104, 4096, 5404, 7131, 9410, 12416, 16384, 21618, 28526, 37640, 49667, 65536, 86475, 114104, 150562, 198668, 262144, 345901, 456419, 602248, 794672, 1048576
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A005533.

Programs

  • Magma
    seq := [Floor(4^(n/5)) : n in [0..50]]; seq; // Vincenzo Librandi, Jun 11 2025
  • Maple
    a:= n-> floor(4^(n/5)):
seq(a(n), n=0..50);  # Alois P. Heinz, Jun 11 2025
  • Mathematica
    Table[Floor[(4^(1/5))^n],{n,0,35}] (* Vincenzo Librandi, Jun 11 2025 *)

A018124 Powers of fifth root of 4 rounded to nearest integer.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 64, 84, 111, 147, 194, 256, 338, 446, 588, 776, 1024, 1351, 1783, 2353, 3104, 4096, 5405, 7132, 9410, 12417, 16384, 21619, 28526, 37641, 49667, 65536, 86475
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A005533.

Programs

  • Python
    from gmpy2 import iroot_rem
def A018124(n):
    i, j = iroot_rem(1<<(n<<1),5)
    return int(i)+int(j<<5>=10*i*((i*((i*(i+1)<<1)+1)<<2)+1)+1) # Chai Wah Wu, Jun 20 2024
Showing 1-4 of 4 results.

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

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