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

0,3

Links

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

Index entries for sequences related to primorial base

Formula

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

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

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); };
A353632(n) = A353630(n+n);

Crossrefs

Even bisection of A353630. A353631 gives the odd bisection.

Cf. A000035, A327860.

Cf. also A353487, A353642.

Sequence in context: A356582 A320839 A094314 * A365713 A348328 A036864

Adjacent sequences: A353629 A353630 A353631 * A353633 A353634 A353635

Keyword

nonn,base

Author

Antti Karttunen, May 01 2022

Status

approved