A369461 - OEIS

%I #15 Nov 20 2024 14:10:26

%S 0,0,0,0,1,0,0,1,1,0,0,0,2,0,0,1,1,1,0,0,2,0,1,0,0,0,0,1,2,1,0,0,3,0,

%T 0,0,2,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,3,0,0,1,1,2,0,0,2,1,1,0,1,0,0,1,

%U 2,0,0,1,3,0,0,0,1,0,0,0,0,0,2,1,2,1,0,1,1,0,0,0,4,0,1,1,0,0,0,1,2,0,1,0,0

%N Number of representations of 12n-5 as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

%C The sequence seems to contain an infinite number of zeros. See A369451 for the cumulative sum, and comments there.

%C Question: Are there any sections of this sequence, with parameters k >= 2, 0 <= i < k, for which a((k*n)-i) = 0 for all n >= 1? - _Antti Karttunen_, Nov 20 2024

%H Antti Karttunen, <a href="/A369461/b369461.txt">Table of n, a(n) for n = 1..100000</a>

%F a(n) = A369054(A017605(n-1)) = A369054((12*n)-5).

%F a(n) = A369055((3*n)-1).

%o (PARI)

%o A369054(n) = if(3!=(n%4),0, my(v = [3,3], ip = #v, r, c=0); while(1, r = (n-(v[1]*v[2])) / (v[1]+v[2]); if(r < v[2], ip--, ip = #v; if(1==denominator(r) && isprime(r),c++)); if(!ip, return(c)); v[ip] = nextprime(1+v[ip]); for(i=1+ip,#v,v[i]=v[i-1])));

%o A369461(n) = A369054((12*n)-5);

%Y Trisection of A369055.

%Y Cf. A017605, A369054, A369451 (partial sums), A369460, A369462.

%K nonn

%O 1,13

%A _Antti Karttunen_, Jan 23 2024