A098015 Indices x such that (1/2)(prime(x+1) - prime(x)) is prime.

4, 6, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 48, 50, 51, 53, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 67, 68, 70, 71, 73, 74, 75, 76, 78, 80, 82, 84, 85, 86, 88, 90, 93, 95, 96, 100, 101, 102, 103, 105, 106, 107, 108

Offset: 1

Author

Cino Hilliard, Sep 09 2004

Keywords

• easy
• nonn

Examples

			Difference between prime(4) and prime(4+1) = 4. 1/2(4) = 2. So 4 is first entry in the table.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

R:= NULL: count:= 0:
p:= 3:
for i from 2 while count < 100 do
  q:= p; p:= nextprime(p);
  if isprime((p-q)/2) then R:= R,i; count:= count+1 fi
od:
R; # Robert Israel, Sep 27 2023

Mathematica

Flatten[Position[(#[[2]]-#[[1]])/2&/@Partition[Prime[Range[200]],2,1],?PrimeQ]] (* _Harvey P. Dale, Dec 14 2012 *)

PARI

f(n) = for(x=1,n,y=prime(x+1)-prime(x);if(isprime(y\2),print1(x",")))