A358842 - OEIS

%I #13 Dec 03 2022 20:26:42

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

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

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

%N a(n) = 1 if A276086(n) is of the form 6k+5, where A276086 is the primorial base exp-function.

%C The XOR-formula involving A358755 corresponds to the XOR-formula given for A353489, which is based on the lemma given in A353516. A similar lemma exists for mod 6 case.

%H Antti Karttunen, <a href="/A358842/b358842.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) = [5 == A276086(n) mod 6], where [ ] is the Iverson bracket.

%F a(n) = A079979(n) - A358841(n) = A059841(n) - A120325(n) - A358841(n).

%F For all n >= 6, a(n) = a(n-6) XOR A358755(n), where XOR is bitwise-XOR, A003987.

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

%Y Characteristic function of A358843.

%Y Cf. A003987, A059841, A079979, A120325, A276086, A358755, A358840, A358841, A358846 [= a(6*n)].

%Y Cf. also A353516, A353489.

%K nonn

%O 0

%A _Antti Karttunen_, Dec 02 2022