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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.
4
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
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
Characteristic function of A344001. Cf. A344000 (positions of zeros).
Even bisection of A354918.
Sequence in context: A295405 A267001 A141735 * A344438 A322585 A326956
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 01 2021
STATUS
approved