cp's OEIS Frontend

A056155 Positive integer k, 1 <= k <= n, which maximizes k^(n+1-k).

%I A056155 #21 Jan 09 2023 07:10:48
%S A056155 1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,
%T A056155 10,10,11,11,11,11,12,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,
%U A056155 15,16,16,16,16,16,17,17,17,17,17,18,18,18,18,18,19,19,19,19,19,20,20,20
%N A056155 Positive integer k, 1 <= k <= n, which maximizes k^(n+1-k).
%C A056155 a(n) is within 1 of x, where n+1 = x*(1 + log(x)).
%H A056155 Seiichi Manyama, <a href="/A056155/b056155.txt">Table of n, a(n) for n = 1..10000</a>
%F A056155 a(n) ~ e^(LambertW(e*(n + 1)) - 1). - _Mats Granvik_, Jan 26 2017
%e A056155 a(5) = 3 because 3^(5+1-3) = 27 is larger than k^(5+1-k) for any other k (1 <= k <= n) besides k = 3.
%t A056155 nn = 79; Monitor[a = Table[RankedMax[Table[k^(n + 1 - k), {k, 1, n}], 1], {n, 1, nn}];, n] Monitor[b = Flatten[Table[Position[Table[k^(n + 1 - k), {k, 1, n}], a[[n]]], {n, 1, nn}]], n] (* _Mats Granvik_, Jan 26 2017 *)
%t A056155 a[n_] := MaximalBy[Range[n], #^(n + 1 - #)&][[1]];
%t A056155 Array[a, 100] (* _Jean-François Alcover_, Dec 11 2020 *)
%o A056155 (PARI) a(n) = my(v = vector(n, k, k^(n+1-k))); vecsort(v,,1)[#v]; \\ _Michel Marcus_, Jan 28 2017
%Y A056155 Cf. A003320.
%K A056155 easy,nonn
%O A056155 1,2
%A A056155 _Leroy Quet_, Jul 30 2000