A354921 Positions of odd terms in A182665.

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

Author

Antti Karttunen, Jun 12 2022

Keywords

• nonn

Comments

Numbers k such that the parity of A344005(k) differs from the parity of k itself.

Crossrefs

Cf. A182665, A344005, A354920 (characteristic function), A354922 (complement).

Cf. also A354919.

Programs

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