A224979 Number of primes of the form p-q+1 where q is any prime < p = prime(n).

0, 1, 1, 2, 2, 3, 4, 4, 6, 6, 4, 3, 8, 6, 10, 10, 12, 5, 4, 12, 9, 8, 16, 18, 6, 16, 10, 16, 12, 20, 6, 18, 16, 14, 24, 8, 9, 10, 26, 22, 28, 12, 22, 13, 26, 16, 12, 14, 24, 18, 30, 36, 16, 32, 28, 32, 38, 14, 13, 32, 16, 38, 16, 34, 17, 30, 12, 18, 32, 26

Offset: 1

Author

Jayanta Basu, Apr 22 2013

Keywords

• nonn

Examples

			For n=5, p=11, there are a(5)=2 solutions: 11-5+1=7 and 11-7+1=5.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A224748, A224908.

Programs

Mathematica

Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p - Prime[i] + 1], c = c + 1]; i++]; c, {n, 70}]
Table[Count[Prime[n]-Prime[Range[n-1]]+1,?PrimeQ],{n,70}] (* _Harvey P. Dale, Jan 08 2015 *)

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