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

Author

Antti Karttunen, Jun 12 2022

Keywords

• nonn

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).

Crossrefs

Positions of zeros in A354920.

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

Programs

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