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

1,6

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.

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000194, A105209, A255270.

Sequence in context: A355480 A390765 A076303 * A343356 A242253 A071839

Adjacent sequences: A339273 A339274 A339275 * A339277 A339278 A339279

Keyword

nonn,easy

Author

Amiram Eldar, Dec 13 2020

Status

approved