A017981 Powers of cube root of 2 rounded up.

1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 11, 13, 16, 21, 26, 32, 41, 51, 64, 81, 102, 128, 162, 204, 256, 323, 407, 512, 646, 813, 1024, 1291, 1626, 2048, 2581, 3251, 4096, 5161, 6502, 8192, 10322, 13004, 16384, 20643, 26008, 32768, 41286, 52016, 65536, 82571, 104032

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A017979.

Programs

Magma

[Ceiling(2^(n/3)): n in [1..60]]; // Vincenzo Librandi, Jan 05 2014

Mathematica

Table[Ceiling[(2^(1/3))^n], {n, 0, 300}] (* Vincenzo Librandi, Jan 05 2014 *)

PARI

a(n) = ceil(sqrtn(2, 3)^n); \\ Michel Marcus, Jan 03 2014

Python

def icbrt(a):
    sr = 1 << (int.bit_length(int(a)) >> 1)
    while a < sr*sr*sr:  sr>>=1
    b = sr>>1
    while b:
      s = sr+b
      if a >= s*s*s:  sr = s
      b>>=1
    return sr
for n in range(100):  print(1+icbrt(2**n-1), end=",")
# Alex Ratushnyak, Jan 04 2014

Extensions

a(44)-a(50) from Alex Ratushnyak, Jan 02 2014