A353632 Even bisection of A353630: Arithmetic derivative of primorial base exp-function, reduced modulo 4, computed for even numbers.

0, 1, 2, 1, 0, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 1, 2, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 3, 0, 1, 2, 1, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 1, 2, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1

Offset: 0

Author

Antti Karttunen, May 01 2022

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Even bisection of A353630. A353631 gives the odd bisection.

Cf. A000035, A327860.

Cf. also A353487, A353642.

Programs

PARI

A353630(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); ((s*m)%4); };
A353632(n) = A353630(n+n);

Formula

a(n) = A353630(2*n) = A010873(A327860(2*n)).

A000035(a(n)) = A000035(n).