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A354922 Positions of even terms in A182665.

%I A354922 #15 Jun 17 2022 16:06:12
%S A354922 1,6,10,14,15,18,20,22,24,26,33,34,36,38,42,45,46,50,51,52,54,58,62,
%T A354922 63,65,68,69,70,72,74,77,78,82,84,86,87,88,91,94,95,96,98,100,106,110,
%U A354922 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
%N A354922 Positions of even terms in A182665.
%C A354922 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).
%o A354922 (PARI)
%o A354922 A354920(n) = forstep(x=n-1,0,-1,if(!((x*(x-1))%n),return(x%2)));
%o A354922 isA354922(n) = !A354920(n);
%o A354922 (Python 3.8+)
%o A354922 from itertools import combinations, islice, count
%o A354922 from math import prod
%o A354922 from sympy import factorint
%o A354922 from sympy.ntheory.modular import crt
%o A354922 def A354922_gen(startvalue=1): # generator of terms >= startvalue
%o A354922     if startvalue <= 1:
%o A354922         yield 1
%o A354922     for n in count(max(startvalue,2)):
%o A354922         plist = tuple(p**q for p, q in factorint(n).items())
%o A354922         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:
%o A354922             yield n
%o A354922 A354922_list = list(islice(A354922_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A354922 Positions of zeros in A354920.
%Y A354922 Cf. A000035, A182665, A344005, A354918, A354921 (complement).
%K A354922 nonn
%O A354922 1,2
%A A354922 _Antti Karttunen_, Jun 12 2022