A204580 Number of primes of the form A204142[i]*A204142[j]+2 (i,j <= n), larger than A204142[n].

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 15, 17, 20, 24, 27, 30, 32, 32, 34, 36, 39, 41, 43, 46, 50, 51, 54, 60, 64, 68, 71, 76, 78, 80, 83, 86, 92, 93, 98, 101, 104, 106, 109, 113, 114, 117, 126, 128, 133, 135, 139, 143, 147, 150, 160, 166, 173, 181

Offset: 1

Author

M. F. Hasler, Feb 11 2012

Keywords

• nonn

Comments

It is not yet known whether there is a finite number of "good numbers" A204142. This is equivalent to the question whether this sequence will eventually decrease to zero.

One has a(100)=408, a(316)=2179, a(1000)=13136, a(3162)=86603, a(10000)=609377.

Links

• M. F. Hasler, Table of n, a(n) for n = 1..3000

Programs

PARI

A204580(n)={ my(r=1,s); while( A204142[r]^2+2<=A204142[n], r++); s=r; sum(i=r,n, while(s>1 & A204142[s-1]*A204142[i]+2 > A204142[n],s--); sum(j=s,i, is/*pseudo*/prime(A204142[j]*A204142[i]+2)))} /* From n~3000 on, use of ispseudoprime is significantly faster. The vector A204142 must be already computed. */