A358846 - OEIS

%I #13 Dec 03 2022 16:52:36

%S 0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,

%T 0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,

%U 0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1

%N a(n) = 1 if A276086(6*n) == 5 (mod 6), otherwise 0, where A276086 is the primorial base exp-function.

%C Question: Are 0's and 1's evenly distributed? Exactly 50/50? See also A358847.

%H Antti Karttunen, <a href="/A358846/b358846.txt">Table of n, a(n) for n = 0..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%F a(n) = [A276086(6*n) == 5 (mod 6)], where [ ] is the Iverson bracket.

%F a(n) = A358842(6*n).

%F a(0) = 0, and for n > 0, a(n) = a(n-1) XOR A358847(n), where XOR is bitwise-XOR, A003987. See comments in A358842.

%o (PARI)

%o A358842(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (5==(m%6)); };

%o A358846(n) = A358842(6*n);

%Y Characteristic function of A358844, whose complement A358845 gives the positions of zeros.

%Y Cf. A003987, A276086, A358840, A358842, A358847.

%K nonn

%O 0

%A _Antti Karttunen_, Dec 03 2022