A017979 Powers of cube root of 2 rounded down.

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50, 64, 80, 101, 128, 161, 203, 256, 322, 406, 512, 645, 812, 1024, 1290, 1625, 2048, 2580, 3250, 4096, 5160, 6501, 8192, 10321, 13003, 16384, 20642, 26007, 32768, 41285, 52015, 65536, 82570, 104031

Offset

0,4

Comments

Rounding has no effect when n is a multiple of 3, because then obviously (2^(1/3))^n = 2^(n/3). - Alonso del Arte, Jan 04 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Example

a(2) = 1 because the cube root of 2 squared is 1.5874...
a(3) = 2 because the cube root of 2 cubed is 2 exactly.
a(4) = 2 because the cube root of 2 to the fourth power is 2.519842...

Mathematica

Table[Floor[(2^(1/3))^n], {n, 0, 49}] (* Alonso del Arte, Jan 04 2014 *)

Prog

(Magma) [Floor(2^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014
(Python)
from sympy import integer_nthroot
def A017979(n): return integer_nthroot(1<<n, 3)[0] # Chai Wah Wu, Jun 18 2024

Crossrefs

Cf. A017981, A002580.

Sequences of the type: Powers of cube root of (k) rounded down: this sequence (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), A017994 (k=7), A018000 (k=9), A018003 (k=10), A018006 (k=11), A018009 (k=12), A018012 (k=13), A018015 (k=14), A018018 (k=15), A018021 (k=16), A018024 (k=17), A018027 (k=18), A018030 (k=19), A018033 (k=20), A018036 (k=21), A018039 (k=22), A018042 (k=23), A018045 (k=24).

Sequence in context: A179241 A316082 A157046 * A140881 A316081 A238708

Adjacent sequences: A017976 A017977 A017978 * A017980 A017981 A017982

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(44)-a(50) from Alex Ratushnyak, Jan 04 2014

Status

approved