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A353526 The smallest prime not dividing n, reduced modulo 4.

%I A353526 #14 Jul 25 2022 22:41:55
%S A353526 2,3,2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,3,2,3,2,3,
%T A353526 2,1,2,3,2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,3,2,3,2,3,2,1,2,3,
%U A353526 2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,1,2,3,2,3,2,3,2,3,2,3,2,1,2,3,2,3,2,1,2,3,2
%N A353526 The smallest prime not dividing n, reduced modulo 4.
%H A353526 Antti Karttunen, <a href="/A353526/b353526.txt">Table of n, a(n) for n = 1..65537</a>
%F A353526 a(n) = A010873(A053669(n)).
%F A353526 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} ((p mod 4)*(p-1)/(Product_{q prime, q <= p} q)) = 2.2324714414... . - _Amiram Eldar_, Jul 25 2022
%t A353526 a[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; Mod[p, 4]]; Array[a, 100] (* _Amiram Eldar_, Jul 25 2022 *)
%o A353526 (PARI)
%o A353526 A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
%o A353526 A353526(n) = (A053669(n)%4);
%Y A353526 Cf. A010873, A053669, A353486, A353516, A353528, A353529.
%Y A353526 Cf. A007395, A353527 (bisections).
%K A353526 nonn
%O A353526 1,1
%A A353526 _Antti Karttunen_, Apr 24 2022