OFFSET
1,8
COMMENTS
In the case of the numbers of the form 12m+11 (i.e., intersection of numbers of the form 3k+2 with the numbers of the form 4m+3) any such representation must be one of the four most common combinations that p, q and r may obtain mod-3-wise (see the table given in comments of A369252), therefore this sequence grows fastest among A369450(n), A369451(n) and a(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])));
A369452list(up_to) = { my(v=vector(up_to)); s = 0; for(n=1, up_to, s+=A369462(n); v[n] = s); (v); };
v369452 = A369452list(up_to);
A369452(n) = v369452[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 24 2024
STATUS
approved