A358752 a(n) = 1 if A349905(n) == 2 (mod 4), otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n.

0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = 1-A152822(A349905(n)).

a(n) = A353495(A003961(n)).

a(n) = A065043(n) - A358750(n).

a(n) = [3-A010873(A001222(n)) == A010873(A003961(n))], where [ ] is the Iverson bracket.

a(n) = [bigomega(n) == 2*A246260(n) (mod 4)].

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A349905(n) = A003415(A003961(n));
A358752(n) = (2==(A349905(n)%4));
(PARI)
A010873(n) = (n%4);
A358752(n) = (3-A010873(bigomega(n))==A010873(A003961(n)));

Crossrefs

Characteristic function of A358762.

Cf. A001222, A003415, A003961, A010873, A065043, A152822, A246260, A349905, A353495, A358750.

Sequence in context: A359429 A353470 A342753 * A368913 A354820 A188086

Adjacent sequences: A358749 A358750 A358751 * A358753 A358754 A358755

Keyword

nonn

Author

Antti Karttunen, Nov 29 2022

Status

approved