%I #11 May 05 2022 09:45:42

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A353630/b353630.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

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

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

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

%o (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); };

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

%Y Cf. A353631, A353632 (bisections).

%Y Cf. also A353486.

%K nonn,base

%O 0,5

%A _Antti Karttunen_, May 01 2022