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A354921
Positions of odd terms in A182665.
5
2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 21, 23, 25, 27, 28, 29, 30, 31, 32, 35, 37, 39, 40, 41, 43, 44, 47, 48, 49, 53, 55, 56, 57, 59, 60, 61, 64, 66, 67, 71, 73, 75, 76, 79, 80, 81, 83, 85, 89, 90, 92, 93, 97, 99, 101, 102, 103, 104, 105, 107, 108, 109, 111, 113, 117, 119, 120, 121, 124, 125, 126, 127, 128
OFFSET
1,1
COMMENTS
Numbers k such that the parity of A344005(k) differs from the parity of k itself.
PROG
(PARI)
A354920(n) = forstep(x=n-1, 0, -1, if(!((x*(x-1))%n), return(x%2)));
isA354921(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 A354921_gen(startvalue=2): # generator of terms >= startvalue
for n in count(max(startvalue, 2)):
plist = tuple(p**q for p, q in factorint(n).items())
if len(plist) == 1 or (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
A354921_list = list(islice(A354921_gen(), 40)) # Chai Wah Wu, Jun 12 2022
CROSSREFS
Cf. A182665, A344005, A354920 (characteristic function), A354922 (complement).
Cf. also A354919.
Sequence in context: A334298 A364160 A304686 * A085233 A357861 A133813
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 12 2022
STATUS
approved