A354918 a(n) = A344005(n) mod 2, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = A000035(A344005(n)).

a(n) = A000035(n) XOR A354920(n), where XOR is bitwise-XOR, A003987.

Prog

(PARI) A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));
(Python 3.8+)
from itertools import combinations
from math import prod
from sympy import factorint
from sympy.ntheory.modular import crt
def A354918(n):
    if n == 1:
        return 1
    plist = tuple(p**q for p, q in factorint(n).items())
    return (n-1 if len(plist) == 1 else int(min(min(crt((m, n//m), (0, -1))[0], crt((n//m, m), (0, -1))[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))))) & 1 # Chai Wah Wu, Jun 12 2022

Crossrefs

Characteristic function of A354919. Parity of A344005.

Cf. A000035, A002378, A003987, A343999 (even bisection), A354920.

Sequence in context: A342025 A353518 A353687 * A354108 A181101 A379274

Adjacent sequences: A354915 A354916 A354917 * A354919 A354920 A354921

Keyword

nonn

Author

Antti Karttunen, Jun 12 2022

Status

approved