A353632 - OEIS

%I #11 May 05 2022 10:04:27

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A353632/b353632.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) = A353630(2*n) = A010873(A327860(2*n)).

%F A000035(a(n)) = A000035(n).

%o (PARI)

%o 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); };

%o A353632(n) = A353630(n+n);

%Y Even bisection of A353630. A353631 gives the odd bisection.

%Y Cf. A000035, A327860.

%Y Cf. also A353487, A353642.

%K nonn,base

%O 0,3

%A _Antti Karttunen_, May 01 2022