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A354922
Positions of even terms in A182665.
3
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).
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 12 2022
STATUS
approved