login
A353527
The smallest prime not dividing 2*n, reduced modulo 4.
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
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.
Sequence in context: A154595 A144437 A169609 * A220670 A264526 A138071
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 24 2022
STATUS
approved