OFFSET
1,4
COMMENTS
In the case of the numbers of the form 12m+3 (i.e., multiples of 3 among the numbers of the form 4m+3) any such representation must either have p = q = 3, or p == q == r == +1 (mod 3), or -1 (mod 3) for all three primes (see the table given in comments of A369252), therefore the cumulative sum here has an intermediate growth among a(n), A369451(n) and A369452(n).
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
PROG
(PARI)
up_to = 1024; \\ 2*(10^4);
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])));
A369450list(up_to) = { my(v=vector(up_to)); s = 0; for(n=1, up_to, s+=A369460(n); v[n] = s); (v); };
v369450 = A369450list(up_to);
A369450(n) = v369450[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 24 2024
STATUS
approved