|
%I #14 Jul 25 2022 22:41:59
%S 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,
%T 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,
%U 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
%N The smallest prime not dividing 2*n, reduced modulo 4.
%H Antti Karttunen, <a href="/A353527/b353527.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A353526(2*n) = A010873(A053669(2*n)).
%F For n >= 1, a(n) = (A353487(n) * A353517(n)) mod 4.
%F 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
%t a[n_] := Module[{p = 2}, While[Divisible[2*n, p], p = NextPrime[p]]; Mod[p, 4]]; Array[a, 100] (* _Amiram Eldar_, Jul 25 2022 *)
%o (PARI)
%o A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
%o A353527(n) = (A053669(2*n)%4);
%Y Bisection of A353526.
%Y Cf. A010873, A053669, A353487, A353517, A353528, A353529.
%K nonn
%O 1,1
%A _Antti Karttunen_, Apr 24 2022
|
