A353630 Arithmetic derivative of primorial base exp-function, reduced modulo 4.

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

Cf. A010873, A166486 (parity of terms), A276086, A327860, A328572, A353493, A353640.

Cf. A353631, A353632 (bisections).

Cf. also A353486.

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); };

Formula

a(n) = A010873(A327860(n)).

a(n) = A353493(A276086(n)).

a(n) = A010873(A328572(n)*A353640(n)). [Note that all terms of A328572 are odd]