A354922 Positions of even terms in A182665.

1, 6, 10, 14, 15, 18, 20, 22, 24, 26, 33, 34, 36, 38, 42, 45, 46, 50, 51, 52, 54, 58, 62, 63, 65, 68, 69, 70, 72, 74, 77, 78, 82, 84, 86, 87, 88, 91, 94, 95, 96, 98, 100, 106, 110, 112, 114, 115, 116, 118, 122, 123, 134, 136, 140, 141, 142, 143, 145, 146, 148, 150, 152, 153, 156, 158, 159, 160, 161, 162, 164, 166

Offset

1,2

Comments

Numbers k such that the parity of A344005(k) is the same as the parity of k itself, or in other words, numbers k for which A354918(k) = A000035(k).

Links

Table of n, a(n) for n=1..72.

Prog

(PARI)
A354920(n) = forstep(x=n-1, 0, -1, if(!((x*(x-1))%n), return(x%2)));
isA354922(n) = !A354920(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 A354922_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 and not (n-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
A354922_list = list(islice(A354922_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Positions of zeros in A354920.

Cf. A000035, A182665, A344005, A354918, A354921 (complement).

Sequence in context: A057714 A143907 A132982 * A300080 A069169 A230766

Adjacent sequences: A354919 A354920 A354921 * A354923 A354924 A354925

Keyword

nonn

Author

Antti Karttunen, Jun 12 2022

Status

approved