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A369462
Number of representations of 12n-1 as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.
8
0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 1, 3, 1, 1, 2, 5, 0, 1, 0, 2, 2, 2, 1, 4, 1, 3, 0, 3, 1, 2, 2, 3, 0, 2, 1, 8, 1, 1, 1, 4, 2, 2, 3, 3, 0, 4, 0, 4, 1, 1, 4, 3, 1, 3, 1, 6, 2, 3, 0, 5, 3, 1, 2, 6, 2, 6, 2, 2, 0, 1, 1, 5, 1, 2, 1, 10, 1, 3, 1, 3, 4, 2, 1, 6, 3, 6, 1, 4, 1, 3, 1, 5, 2, 3, 0
OFFSET
1,10
COMMENTS
See A369452 for the cumulative sum, and comments there.
Question: Is there only a finite number of 0's in this sequence? See discussion at A369055 and see A369463 for empirical data.
LINKS
FORMULA
a(n) = A369054(A017653(n-1)) = A369054(12*n - 1).
a(n) = A369055(3*n).
PROG
(PARI)
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])));
A369462(n) = A369054((12*n)-1);
CROSSREFS
Trisection of A369055.
Cf. A017653, A369054, A369252, A369452 (partial sums), A369460, A369461, A369463 (= (12*i)-1, where i are the indices of zeros in this sequence).
Sequence in context: A193690 A108964 A036581 * A135055 A265433 A298247
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 23 2024
STATUS
approved