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

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to primorial base

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]

Prog

(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); };

Crossrefs

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

Cf. A353631, A353632 (bisections).

Cf. also A353486.

Sequence in context: A033804 A103910 A155993 * A341091 A210806 A147867

Adjacent sequences: A353627 A353628 A353629 * A353631 A353632 A353633

Keyword

nonn,base

Author

Antti Karttunen, May 01 2022

Status

approved