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A354919
Positions of odd terms in A344005.
5
1, 2, 4, 8, 12, 15, 16, 28, 30, 32, 33, 40, 44, 45, 48, 51, 56, 60, 63, 64, 65, 66, 69, 76, 77, 80, 87, 90, 91, 92, 95, 102, 104, 108, 115, 120, 123, 124, 126, 128, 130, 132, 138, 141, 143, 144, 145, 153, 154, 159, 161, 172, 174, 175, 177, 180, 182, 184, 187, 188, 189, 190, 192, 195, 204, 207, 213, 215, 221, 224
OFFSET
1,2
COMMENTS
Numbers k such that the parity of A182665(k) differs from the parity of k itself.
PROG
(PARI)
A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));
isA354919(n) = A354918(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 A354919_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:
if (n-1) & 1: yield n
elif 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
A354919_list = list(islice(A354919_gen(), 40)) # Chai Wah Wu, Jun 12 2022
CROSSREFS
Cf. A002378, A182665, A344005, A354918 (characteristic function).
Cf. also A354921.
Sequence in context: A064711 A050865 A354109 * A288514 A350616 A282667
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 12 2022
STATUS
approved