A255849 Characteristic function of pentagonal numbers.

1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset

0

Comments

Pentagonal numbers are of the form (3*n^2-n)/2.

Links

Antti Karttunen, Table of n, a(n) for n = 0..101270

Index entries for characteristic functions

Formula

For n > 0, a(n) = floor(sqrt(2*n/3+1/36)+1/6)-floor(sqrt(2*(n-1)/3+1/36)+1/6).

For n>0, a(n) = 1 if n=m*(3*m-1)/2 and a(n) = 0 otherwise where m = floor(sqrt(2n/3))+1. - Chai Wah Wu, Oct 02 2025

Mathematica

Join[{1}, Table[If[IntegerQ[(1+Sqrt[1+24n])/6], 1, 0], {n, 100}]] (* Harvey P. Dale, Feb 25 2018 *)
Module[{nn=20, n5}, n5=PolygonalNumber[5, Range[0, nn]]; Table[If[MemberQ[ n5, n], 1, 0], {n, 0, n5[[-1]]}]] (* Harvey P. Dale, Dec 30 2021 *)

Prog

(PARI) a(n) = ispolygonal(n, 5); \\ Michel Marcus, Aug 04 2023
(Python)
from math import isqrt
def A255849(n): return int((m:=isqrt((k:=n<<1)//3)+1)*(3*m-1)==k) if n else 1 # Chai Wah Wu, Oct 02 2025

Crossrefs

Characteristic function of A000326.

Cf. A080995, A180446.

Sequence in context: A378454 A256436 A253903 * A379117 A185059 A179776

Adjacent sequences: A255846 A255847 A255848 * A255850 A255851 A255852

Keyword

nonn

Author

Mikael Aaltonen, Mar 08 2015

Extensions

More terms from Antti Karttunen, Dec 15 2024

Status

approved