A368941 a(n) = floor(3/2 + sqrt(n)).

1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

0,2

Comments

Burning number of the n-ladder (for n >= 1), n-Moebius ladder (for n >= 3), and n-prism (for n >= 3) graphs.

Except for the first term, n+1 appears 2n times for n>0. - Chai Wah Wu, Feb 11 2026

Links

Table of n, a(n) for n=0..85.

Eric Weisstein's World of Mathematics, Burning Number.

Eric Weisstein's World of Mathematics, Ladder Graph.

Eric Weisstein's World of Mathematics, Moebius Ladder.

Eric Weisstein's World of Mathematics, Prism Graph.

Formula

a(n) = A000194(n) + 1. - Andrew Howroyd, Jan 10 2024

G.f.: x*(1 + QPochhammer(-x^2, x^4)*QPochhammer(x^8, x^8))/(1 - x).

Mathematica

Table[Floor[3/2 + Sqrt[n]], {n, 50}]
Floor[3/2 + Sqrt[Range[50]]]
CoefficientList[Series[(1 + QPochhammer[-x^2, x^4]  QPochhammer[x^8, x^8])/(1 - x), {x, 0, 50}], x]

Prog

(PARI) apply( {A368941(n)=sqrtint(4*n)\/2+1}, [0..99]) \\ M. F. Hasler, Nov 06 2025
(Python)
from math import isqrt
def A368941(n): return (m:=isqrt(n))+(n>m*(m+1))+1 # Chai Wah Wu, Feb 11 2026

Crossrefs

Sequence agrees with the known terms of A155934.

Cf. A000194, A003059.

Sequence in context: A316843 A331246 A331256 * A283297 A091194 A156079

Adjacent sequences: A368938 A368939 A368940 * A368942 A368943 A368944

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 10 2024

Extensions

Terms a(26) and beyond from Andrew Howroyd, Jan 10 2024

Status

approved