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

1,1

Comments

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

Links

Table of n, a(n) for n=1..76.

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

Adjacent sequences: A354918 A354919 A354920 * A354922 A354923 A354924

Keyword

nonn

Author

Antti Karttunen, Jun 12 2022

Status

approved