cp's OEIS Frontend

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

%I A215892 #30 Sep 08 2022 08:46:03
%S A215892 0,5,0,7,28,79,192,431,24,717,2368,5995,13640,29393,0,47551,157168,
%T A215892 393967,888576,1902671,3960048,1952265,8814592,23788807,55227488,
%U A215892 119868821,251225088,516359763,344741824,1259979967,3221225472,7298466623,15635064768
%N A215892 a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k.
%H A215892 Vincenzo Librandi, <a href="/A215892/b215892.txt">Table of n, a(n) for n = 2..1000</a>
%F A215892 a(n) = 2^n - n^floor(n*log_n(2)), where log_n is the base-n logarithm.
%e A215892 a(2) = 2^2 - 2^2 = 0,
%e A215892 a(3) = 2^3 - 3 = 5,
%e A215892 a(4) = 2^4 - 4^2 = 0,
%e A215892 a(5) = 2^5 - 5^2 = 7,
%e A215892 a(6)..a(9) are 2^n - n^2,
%e A215892 a(10)..a(15) are 2^n - n^3,
%e A215892 a(16)..a(22) are 2^n - n^4, and so on.
%t A215892 Table[2^n - n^Floor[n*Log[n, 2]], {n, 2, 35}] (* _T. D. Noe_, Aug 27 2012 *)
%o A215892 (Python)
%o A215892 for n in range(2,100):
%o A215892     a = 2**n
%o A215892     k = 0
%o A215892     while n**(k+1) <= a:
%o A215892         k += 1
%o A215892     print(a - n**k, end=',')
%o A215892 (Magma) [2^n - n^Floor(n*Log(n, 2)): n in [2..40]]; // _Vincenzo Librandi_, Jan 14 2019
%Y A215892 Cf. A000325, A024012, A024013, A024014, A024015, A024016.
%Y A215892 Cf. A024017, A024018, A024019, A024020, A024021, A024022.
%Y A215892 Cf. A060508.
%K A215892 nonn
%O A215892 2,2
%A A215892 _Alex Ratushnyak_, Aug 25 2012