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A353529
a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 4m+3, otherwise a(n) = 0.
10
0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1
OFFSET
1
FORMULA
If A353526(n) = 3 [A053669(n) is in A002145], then a(n) = 1, otherwise a(n) = 0.
For all n >= 2, a(n) = A353489(n) XOR A353489(n-2), where XOR is bitwise-XOR, A003987.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime, p == 3 (mod 4)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.3662357207... . - Amiram Eldar, Jul 25 2022
MATHEMATICA
f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; a[n_] := If[Mod[f[n], 4] == 3, 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 25 2022 *)
PROG
(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353529(n) = (3==(A053669(n)%4));
CROSSREFS
Characteristic function of A353531.
Differs from A353525 for the first time at n=210, where a(210) = 1, while A353525(210) = 0.
Sequence in context: A157687 A189668 A353525 * A286907 A284851 A289741
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 24 2022
STATUS
approved