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

1,2

Comments

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

Links

Table of n, a(n) for n=1..70.

Prog

(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

Crossrefs

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

Cf. also A354921.

Sequence in context: A064711 A050865 A354109 * A288514 A350616 A282667

Adjacent sequences: A354916 A354917 A354918 * A354920 A354921 A354922

Keyword

nonn

Author

Antti Karttunen, Jun 12 2022

Status

approved