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A215892 a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k. 2
0, 5, 0, 7, 28, 79, 192, 431, 24, 717, 2368, 5995, 13640, 29393, 0, 47551, 157168, 393967, 888576, 1902671, 3960048, 1952265, 8814592, 23788807, 55227488, 119868821, 251225088, 516359763, 344741824, 1259979967, 3221225472, 7298466623, 15635064768 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

FORMULA

a(n) = 2^n - n^floor(n*log_n(2)), where log_n is the base-n logarithm.

EXAMPLE

a(2) = 2^2 - 2^2 = 0,

a(3) = 2^3 - 3 = 5,

a(4) = 2^4 - 4^2 = 0,

a(5) = 2^5 - 5^2 = 7,

a(6)..a(9) are 2^n - n^2,

a(10)..a(15) are 2^n - n^3,

a(16)..a(22) are 2^n - n^4, and so on.

MATHEMATICA

Table[2^n - n^Floor[n*Log[n, 2]], {n, 2, 35}] (* T. D. Noe, Aug 27 2012 *)

PROG

(Python)

for n in range(2, 100):

    a = 2**n

    k = 0

    while n**(k+1) <= a:

        k += 1

    print(a - n**k, end=', ')

(MAGMA) [2^n - n^Floor(n*Log(n, 2)): n in [2..40]]; // Vincenzo Librandi, Jan 14 2019

CROSSREFS

Cf. A000325, A024012, A024013, A024014, A024015, A024016.

Cf. A024017, A024018, A024019, A024020, A024021, A024022.

Cf. A060508.

Sequence in context: A201417 A147666 A343071 * A200643 A200231 A124914

Adjacent sequences:  A215889 A215890 A215891 * A215893 A215894 A215895

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Aug 25 2012

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)