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

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, 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, 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

Offset

1,13

Comments

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

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

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

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

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])));
A369461(n) = A369054((12*n)-5);

Crossrefs

Trisection of A369055.

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

Sequence in context: A065716 A375107 A079409 * A114643 A369055 A038498

Adjacent sequences: A369458 A369459 A369460 * A369462 A369463 A369464

Keyword

nonn

Author

Antti Karttunen, Jan 23 2024

Status

approved