login
Nearest integer to the fourth root of n.
1

%I #20 Dec 23 2020 04:38:25

%S 1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%T 2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,

%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N Nearest integer to the fourth root of n.

%H Amiram Eldar, <a href="/A339276/b339276.txt">Table of n, a(n) for n = 1..10000</a>

%H Jonathan M. Borwein and others, <a href="https://www.jstor.org/stable/2975334">Nearest Integer Zeta Functions, solution to Problem 10212</a>, The American Mathematical Monthly, Vol. 101, No. 6 (1994), pp. 579-580.

%F Sum_{n>=1} 1/a(n)^s = 4*zeta(s-3) + zeta(s-1), for s>4 (Borwein, 1994).

%e a(1) = 1 since 1^(1/4) = 1.

%e a(6) = 2 since 6^(1/4) = 1.565... and its nearest integer is 2.

%t Table[Round[Surd[n, 4]], {n, 1, 100}]

%Y Cf. A000194, A105209, A255270.

%K nonn,easy

%O 1,6

%A _Amiram Eldar_, Dec 13 2020