OFFSET
1,8
COMMENTS
In the case of the numbers of the form 12m+7 (i.e., intersection of numbers of the form 3k+1 with the numbers of the form 4m+3) any such representation must have p = 3 and q > 3 (see the table given in comments of A369252), therefore the cumulative sum here grows slowest among A369450(n), a(n) and A369452(n). Notably, it seems that a(n) < n for all 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])));
A369451list(up_to) = { my(v=vector(up_to)); s = 0; for(n=1, up_to, s+=A369461(n); v[n] = s); (v); };
v369451 = A369451list(up_to);
A369451(n) = v369451[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 24 2024
STATUS
approved