A224925 a(n) = number of primes of the form p*q-(p+q) where p = prime(n) and q is any prime < p.
0, 0, 2, 3, 2, 4, 2, 4, 3, 2, 7, 4, 5, 8, 2, 4, 2, 8, 7, 6, 11, 7, 6, 5, 10, 4, 11, 4, 11, 5, 14, 6, 6, 12, 4, 17, 10, 14, 5, 4, 4, 14, 6, 12, 9, 14, 24, 14, 7, 14, 11, 6, 21, 11, 6, 7, 6, 23, 15, 13, 18, 8, 18, 11, 22, 8, 29, 16, 11, 22, 9, 7, 21, 19, 26
Offset: 1
Keywords
Examples
a(3)=2 since for the third prime 5 we have 5*2-(5+2)=3 and 5*3-(5+3)=7. Also a(4)=3 since for the fourth prime 7 we have 7*2-(7+2)=5, 7*3-(7+3)=11 and 7*5-(7+5)=23.
Programs
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Mathematica
Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p*Prime[i] - (p + Prime[i])], c = c + 1] i++]; c, {n, 75}]