A343999 a(n) = A011772(n) mod 2, where A011772(n) is the smallest number m such that m(m+1)/2 is divisible by n.

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

Offset

1

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..16383

Index entries for characteristic functions

Formula

a(n) = A000035(A011772(n)) = A354918(2*n). - Antti Karttunen, Jun 14 2022

Prog

(Python)
from sympy.ntheory.modular import crt
from sympy import factorint
from itertools import product
def A343999(n):
    fs = factorint(2*n)
    plist = [p**fs[p] for p in fs]
    return int(min(k for k in (crt(plist, d)[0] for d in product([0, -1], repeat=len(plist))) if k > 0) % 2) # Chai Wah Wu, Jun 01 2021

Crossrefs

Cf. A000035, A011772, A343996, A343997.

Characteristic function of A344001. Cf. A344000 (positions of zeros).

Even bisection of A354918.

Sequence in context: A295405 A267001 A141735 * A344438 A322585 A326956

Adjacent sequences: A343996 A343997 A343998 * A344000 A344001 A344002

Keyword

nonn

Author

N. J. A. Sloane, Jun 01 2021

Status

approved