A353527 The smallest prime not dividing 2*n, reduced modulo 4.

3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3

Offset: 1

Author

Antti Karttunen, Apr 24 2022

Keywords

• nonn

Links

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

Crossrefs

Bisection of A353526.

Cf. A010873, A053669, A353487, A353517, A353528, A353529.

Programs

Mathematica

a[n_] := Module[{p = 2}, While[Divisible[2*n, p], p = NextPrime[p]]; Mod[p, 4]]; Array[a, 100] (* Amiram Eldar, Jul 25 2022 *)

PARI

A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353527(n) = (A053669(2*n)%4);

Formula

a(n) = A353526(2*n) = A010873(A053669(2*n)).

For n >= 1, a(n) = (A353487(n) * A353517(n)) mod 4.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime > 2} ((p mod 4)*(p-1)/(Product_{q prime, q <= p} q)) = 2.4649428829... . - Amiram Eldar, Jul 25 2022