A353529 a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 4m+3, otherwise a(n) = 0.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

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.

Cf. A002145, A003987, A053669, A059841, A353489, A353526, A353528.

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

Adjacent sequences: A353526 A353527 A353528 * A353530 A353531 A353532

Keyword

nonn

Author

Antti Karttunen, Apr 24 2022

Status

approved