A017985 Powers of cube root of 4 rounded down.

1, 1, 2, 4, 6, 10, 16, 25, 40, 64, 101, 161, 256, 406, 645, 1024, 1625, 2580, 4096, 6501, 10321, 16384, 26007, 41285, 65536, 104031, 165140, 262144, 416127, 660561, 1048576, 1664510, 2642245, 4194304, 6658042, 10568983, 16777216, 26632170, 42275935, 67108864

Offset

0,3

Comments

a(n) gives the maximum number of cards that can be mixed by n Gilbert-Shannon-Reeds shuffles, up to a bounded additive correction. This reflects the Bayer-Diaconis cutoff phenomenon, for which the practical mixing time satisfies n ~ (3/2)*log_2(a(n)) + c(n) with c(n) bounded. For practical deck sizes c(n) is typically around -1 or -2; in particular, a(7) = 64 explains the classical "seven shuffles suffice" rule for a 52-card deck. - Felix Huber, May 28 2026

Links

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

Formula

a(n) = floor(4^(n/3)). - Wesley Ivan Hurt, Sep 04 2022

Mathematica

Table[Floor[4^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)

Prog

(Magma) [Floor(4^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014
(Python)
from sympy import integer_nthroot
def A017985(n): return integer_nthroot(1<<(n<<1), 3)[0] # Chai Wah Wu, May 28 2026

Crossrefs

Cf. sequences of the type: Powers of cube root of (k) rounded down A017979 (k=2), A017982 (k=3), this sequence (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).

Cf. A005480.

Sequence in context: A390129 A006305 A067247 * A327474 A347207 A028488

Adjacent sequences: A017982 A017983 A017984 * A017986 A017987 A017988

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jan 06 2014

Status

approved