login
Number of primes of the form p-q+1 where q is any prime < p = prime(n).
2

%I #8 Jan 08 2015 15:45:33

%S 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,

%T 20,6,18,16,14,24,8,9,10,26,22,28,12,22,13,26,16,12,14,24,18,30,36,16,

%U 32,28,32,38,14,13,32,16,38,16,34,17,30,12,18,32,26

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

%H Harvey P. Dale, <a href="/A224979/b224979.txt">Table of n, a(n) for n = 1..1000</a>

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

%t Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p - Prime[i] + 1], c = c + 1]; i++]; c, {n, 70}]

%t Table[Count[Prime[n]-Prime[Range[n-1]]+1,_?PrimeQ],{n,70}] (* _Harvey P. Dale_, Jan 08 2015 *)

%o (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

%Y Cf. A224748, A224908.

%K nonn

%O 1,4

%A _Jayanta Basu_, Apr 22 2013