A339276 Nearest integer to the fourth root of n.

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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Author

Amiram Eldar, Dec 13 2020

Keywords

• nonn
• easy

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jonathan M. Borwein and others, Nearest Integer Zeta Functions, solution to Problem 10212, The American Mathematical Monthly, Vol. 101, No. 6 (1994), pp. 579-580.

Crossrefs

Cf. A000194, A105209, A255270.

Programs

Mathematica

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

Python

from sympy import integer_nthroot
def A339276(n): return (m:=integer_nthroot(n,4)[0])+((n<<4)>=((m<<1)+1)**4) # Chai Wah Wu, Jun 06 2025

Formula

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