A224980 Number of primes of the form p-q-1 where q is any prime < p = prime(n).
0, 0, 1, 1, 3, 2, 4, 4, 5, 4, 6, 8, 6, 8, 7, 6, 7, 12, 12, 10, 12, 14, 9, 8, 14, 12, 16, 11, 16, 14, 20, 14, 10, 16, 10, 24, 22, 20, 11, 12, 13, 28, 16, 22, 18, 26, 38, 22, 13, 24, 14, 18, 36, 18, 16, 17, 18, 38, 32, 28, 32, 16, 30, 24, 34, 20, 48, 38, 17
Offset: 1
Keywords
Examples
For n=5, p=11, there are a(5)=3 solutions: 11-3-1=7, 11-5-1=5, and 11-7-1=3.
Programs
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Mathematica
Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p - Prime[i] - 1], c = c + 1]; i++]; c, {n, 69}] -
PARI
a(n)=my(p=prime(n),s);forprime(q=2,p-1,s+=isprime(p-q-1));s \\ Charles R Greathouse IV, Apr 22 2013