A011093 -id:A011093 - cp's OEIS frontend

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

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

Clark Kimberling, Jan 25 2011

nonn

Cf. A005531, A005533, A011093.

Cf. A184910, A184911, A378142, A378185, A379510.

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 *)

Definition in name corrected by Clark Kimberling, Jan 18 2025

A018135 Powers of fifth root of 8 rounded down.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 12, 18, 27, 42, 64, 97, 147, 222, 337, 512, 776, 1176, 1782, 2702, 4096, 6208, 9410, 14263, 21618, 32768, 49667, 75281, 114104, 172950, 262144, 397336, 602248, 912838, 1383604, 2097152, 3178688, 4817990, 7302707, 11068834, 16777216, 25429504, 38543920, 58421659, 88550676, 134217728

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Cf. A011093.

seq := [Floor(8^(n/5)) : n in [0..60]]; seq; // Vincenzo Librandi, Jun 12 2025

Floor[Surd[8,5]^Range[0,40]] (* Harvey P. Dale, Jun 16 2016 *)
Table[Floor[(8^(1/5))^n],{n,0,50}] (* Vincenzo Librandi, Jun 12 2025 *)

A018136 Powers of fifth root of 8 rounded to nearest integer.

Original entry on oeis.org

1, 2, 2, 3, 5, 8, 12, 18, 28, 42, 64, 97, 147, 223, 338, 512, 776, 1176, 1783, 2702, 4096, 6208, 9410, 14263, 21619, 32768, 49667, 75281, 114105, 172951, 262144, 397336, 602249, 912838, 1383604, 2097152

Offset: 0

N. J. A. Sloane

nonn

Paolo Xausa, Table of n, a(n) for n = 0..1000

Cf. A011093.

Round[(8^(1/5))^Range[0, 50]] (* Paolo Xausa, Jul 01 2024 *)

from gmpy2 import iroot_rem
def A018136(n):
    i, j = iroot_rem(1<<3*n,5)
    return int(i)+int(j<<5>=10*i*((i*((i*(i+1)<<1)+1)<<2)+1)+1) # Chai Wah Wu, Jun 20 2024

cp's OEIS Frontend

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

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A018135 Powers of fifth root of 8 rounded down.

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A018136 Powers of fifth root of 8 rounded to nearest integer.

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cp's OEIS Frontend

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

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Extensions

A018135 Powers of fifth root of 8 rounded down.

Views

Author

Keywords

Links

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Magma

Mathematica

A018136 Powers of fifth root of 8 rounded to nearest integer.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

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