A354919 Positions of odd terms in A344005.

1, 2, 4, 8, 12, 15, 16, 28, 30, 32, 33, 40, 44, 45, 48, 51, 56, 60, 63, 64, 65, 66, 69, 76, 77, 80, 87, 90, 91, 92, 95, 102, 104, 108, 115, 120, 123, 124, 126, 128, 130, 132, 138, 141, 143, 144, 145, 153, 154, 159, 161, 172, 174, 175, 177, 180, 182, 184, 187, 188, 189, 190, 192, 195, 204, 207, 213, 215, 221, 224

Offset: 1

Author

Antti Karttunen, Jun 12 2022

Keywords

• nonn

Comments

Numbers k such that the parity of A182665(k) differs from the parity of k itself.

Crossrefs

Cf. A002378, A182665, A344005, A354918 (characteristic function).

Cf. also A354921.

Programs

PARI

A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));
isA354919(n) = A354918(n);
(Python 3.8+)
from itertools import combinations, islice, count
from math import prod
from sympy import factorint
from sympy.ntheory.modular import crt
def A354919_gen(startvalue=1): # generator of terms >= startvalue
    if startvalue <= 1:
        yield 1
    for n in count(max(startvalue,2)):
        plist = tuple(p**q for p, q in factorint(n).items())
        if len(plist) == 1:
            if (n-1) & 1: yield n
        elif 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:
            yield n
A354919_list = list(islice(A354919_gen(),40)) # Chai Wah Wu, Jun 12 2022