login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215892 a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k. 2

%I #30 Sep 08 2022 08:46:03

%S 0,5,0,7,28,79,192,431,24,717,2368,5995,13640,29393,0,47551,157168,

%T 393967,888576,1902671,3960048,1952265,8814592,23788807,55227488,

%U 119868821,251225088,516359763,344741824,1259979967,3221225472,7298466623,15635064768

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

%H Vincenzo Librandi, <a href="/A215892/b215892.txt">Table of n, a(n) for n = 2..1000</a>

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

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

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

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

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

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

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

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

%t Table[2^n - n^Floor[n*Log[n, 2]], {n, 2, 35}] (* _T. D. Noe_, Aug 27 2012 *)

%o (Python)

%o for n in range(2,100):

%o a = 2**n

%o k = 0

%o while n**(k+1) <= a:

%o k += 1

%o print(a - n**k, end=',')

%o (Magma) [2^n - n^Floor(n*Log(n, 2)): n in [2..40]]; // _Vincenzo Librandi_, Jan 14 2019

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

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

%Y Cf. A060508.

%K nonn

%O 2,2

%A _Alex Ratushnyak_, Aug 25 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)