A215892 a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k.

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

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