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

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, 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, 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

Offset

1,1

Links

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

Formula

a(n) = A010873(A053669(n)).

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

Mathematica

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

Prog

(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353526(n) = (A053669(n)%4);

Crossrefs

Cf. A010873, A053669, A353486, A353516, A353528, A353529.

Cf. A007395, A353527 (bisections).

Sequence in context: A341018 A214323 A321865 * A244544 A159580 A121549

Adjacent sequences: A353523 A353524 A353525 * A353527 A353528 A353529

Keyword

nonn

Author

Antti Karttunen, Apr 24 2022

Status

approved