A014306 a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1.

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

Offset

0,1

Comments

Characteristic function of A145397.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

Example

a(A145397(n))=1; a(A000292(n))=0; a(n)=1-A023533(n). - Reinhard Zumkeller, Oct 14 2008
From David A. Corneth, Oct 01 2018: (Start)
For n = 0, floor((6*0-1) ^ (1/3)) = -1. binomial(-1 + 2, 3) = n so a(0) = 0.
For n = 10, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) = n so a(10) = 0.
For n = 11, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) != n so a(11) = 1. (End)

Prog

(PARI) A014306(n) = { my(k=0); while(binomial(k+2, 3)<n, k++); !(binomial(k+2, 3)==n); }; \\ Antti Karttunen, Sep 30 2018
(PARI) a(n) = if(n==0, return(0)); my(t = sqrtnint(6*n-1, 3)); binomial(t+2, 3) != n \\ David A. Corneth, Oct 01 2018
(PARI) first(n) = my(res = vector(n+1, i, 1), ov = nv = [1, 2, 1, 0]); while(nv[4]<=n, res[nv[4]+1] = 0; for(i = 2, 4, nv[i] = ov[i-1] + ov[i]); ov = nv); res \\ David A. Corneth, Oct 01 2018
(Python)
from math import comb
from sympy import integer_nthroot
def A014306(n): return int(n!=comb(integer_nthroot(6*n, 3)[0]+2, 3)) # Chai Wah Wu, Nov 05 2025

Crossrefs

Cf. A000292, A023533, A145397.

Sequence in context: A165560 A358220 A354874 * A384312 A374220 A335716

Adjacent sequences: A014303 A014304 A014305 * A014307 A014308 A014309

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Data section extended up to a(120) by Antti Karttunen, Sep 30 2018

Status

approved