A373601 - OEIS

%I #16 Jun 18 2024 08:18:58

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

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

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

%N a(n) = 1 if the sum of prime factors (with multiplicity) of A276086(n) is a multiple of 3, otherwise 0, where A276086 is the primorial base exp-function.

%C a(n) = 1 if the multiplicities of prime factors of A276086(n) that are of the form 3m+1 (A002476) and of the form 3m-1 (A003627) are equal modulo 3, otherwise 0.

%C Sum_{i=1..10^n} a(i), for n = 1..9 gives: 2, 32, 332, 3331, 33331, 333332, 3333335, 33333335, 333333332.

%H Antti Karttunen, <a href="/A373601/b373601.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) = A079978(A373600(n)) = A079978(A001414(A276086(n))).

%F a(n) = A373371(A276086(n)).

%o (PARI) A373601(n) = { my(m=1, p=2, c1=0, c2=0); while(n, if(1==(p%3), c1 += (n%p), if(2==(p%3), c2 += (n%p))); n = n\p; p = nextprime(1+p)); 0==((c1-c2)%3); };

%Y Characteristic function of A373602.

%Y Cf. A002476, A003627, A049345, A079978, A276086, A289142, A373371, A373600.

%Y Cf. also A369653, A373604.

%K nonn

%O 0

%A _Antti Karttunen_, Jun 18 2024