A340301 -id:A340301 - cp's OEIS frontend

A326299 a(n) = floor(n*log_2(n)).

0, 2, 4, 8, 11, 15, 19, 24, 28, 33, 38, 43, 48, 53, 58, 64, 69, 75, 80, 86, 92, 98, 104, 110, 116, 122, 128, 134, 140, 147, 153, 160, 166, 172, 179, 186, 192, 199, 206, 212, 219, 226, 233, 240, 247, 254, 261, 268, 275, 282, 289, 296, 303, 310, 317, 325, 332, 339, 347, 354

Offset: 1

Michel Marcus, Oct 17 2019

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Sandor Csörgö, Gordon Simons, On Steinhaus' resolution of the St. Petersburg paradox, Probab. Math. Statist. 14 (1993), 157--172. MR1321758 (96b:60017). See Table 1 p. 171.

Cf. A000523 (log_2(n)), A061717, A340301.

a:= n-> floor(n*log[2](n)):
seq(a(n), n=1..80);  # Alois P. Heinz, Oct 17 2019

Table[Floor[n Log2[n]],{n,80}] (* Harvey P. Dale, Nov 29 2022 *)

PARI
```
a(n) = n*log(n)\log(2);
```

A336018 a(n) = floor(frac(log_2(n))*n), where frac denotes the fractional part.

Original entry on oeis.org

0, 0, 1, 0, 1, 3, 5, 0, 1, 3, 5, 7, 9, 11, 13, 0, 1, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 27, 29, 0, 1, 2, 4, 6, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 0, 1, 2, 4, 5, 7, 9, 10, 12, 13

Offset: 1

Andres Cicuttin, Jul 04 2020

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A000079, A000523, A000195, A336017, A326299, A340301.

a:= n-> floor(n*log[2](n))-n*ilog2(n):
seq(a(n), n=1..80);  # Alois P. Heinz, Jan 04 2021

a[n_]:=Floor[FractionalPart[Log[2, n]]*n];
Table[a[n], {n, 1, 100}]

a(n) = floor(n*frac(log(n)/log(2))); \\ Michel Marcus, Jul 07 2020

def A336018(n):
    return len(bin(n**n//(2**((len(bin(n))-3)*n))))-3 # Chai Wah Wu, Jul 09 2020

a(n) = floor((log_2(n) - floor(log_2(n)))*n).
From Alois P. Heinz, Jan 04 2021: (Start)
a(n) = A326299(n) - A340301(n).
a(n) = 0 <=> n in { A000079 }. (End)

A340298 a(n) = a(floor(n/2)) + a(ceiling(n/2)) + n*floor(log_2(n)) for n >= 2, a(n) = n for n <= 1.

Original entry on oeis.org

0, 1, 4, 8, 16, 22, 28, 38, 56, 65, 74, 83, 92, 105, 118, 139, 176, 189, 202, 215, 228, 241, 254, 267, 280, 297, 314, 331, 348, 373, 398, 439, 512, 530, 548, 566, 584, 602, 620, 638, 656, 674, 692, 710, 728, 746, 764, 782, 800, 822, 844, 866, 888, 910, 932, 954

Offset: 0

Alois P. Heinz, Jan 03 2021

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Cf. A033156, A340257, A340301.

a:= proc(n) option remember; `if`(n<2, n, (h->
      a(h)+a(n-h)+n*ilog2(n))(iquo(n, 2)))
    end:
seq(a(n), n=0..55);

a(2^n) = A340257(n).

cp's OEIS Frontend

A326299 a(n) = floor(n*log_2(n)).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A336018 a(n) = floor(frac(log_2(n))*n), where frac denotes the fractional part.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

A340298 a(n) = a(floor(n/2)) + a(ceiling(n/2)) + n*floor(log_2(n)) for n >= 2, a(n) = n for n <= 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Formula