cp's OEIS Frontend

A369461 Number of representations of 12n-5 as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

%I A369461 #15 Nov 20 2024 14:10:26
%S A369461 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 A369461 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 A369461 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 A369461 Number of representations of 12n-5 as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.
%C A369461 The sequence seems to contain an infinite number of zeros. See A369451 for the cumulative sum, and comments there.
%C A369461 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 A369461 Antti Karttunen, <a href="/A369461/b369461.txt">Table of n, a(n) for n = 1..100000</a>
%F A369461 a(n) = A369054(A017605(n-1)) = A369054((12*n)-5).
%F A369461 a(n) = A369055((3*n)-1).
%o A369461 (PARI)
%o A369461 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 A369461(n) = A369054((12*n)-5);
%Y A369461 Trisection of A369055.
%Y A369461 Cf. A017605, A369054, A369451 (partial sums), A369460, A369462.
%K A369461 nonn
%O A369461 1,13
%A A369461 _Antti Karttunen_, Jan 23 2024