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

1,1

Links

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

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

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 *)

Prog

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

Crossrefs

Bisection of A353526.

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

Sequence in context: A154595 A144437 A169609 * A220670 A264526 A138071

Adjacent sequences: A353524 A353525 A353526 * A353528 A353529 A353530

Keyword

nonn

Author

Antti Karttunen, Apr 24 2022

Status

approved