A098043 - OEIS

%I #16 Jul 08 2024 08:41:32

%S 3,3,7,5,13,11,3,11,7,17,19,17,31,7,37,23,61,5,19,47,31,17,29,7,5,19,

%T 41,31,41,11,79,7,7,23,37,31,13,29,47,13,83,29,13,11,59,17,23,17,11,

%U 61,5,23,83,7,7,79,5,5,31,41,61,5,29,19,19,47,67,7,13,31,29,13,137,61,53,43

%N Primes of the form (prime(prime(k+1)) - prime(prime(k)))/2.

%C Primes of the form A073131(k)/2. - _Amiram Eldar_, Jul 08 2024

%H Amiram Eldar, <a href="/A098043/b098043.txt">Table of n, a(n) for n = 1..10000</a>

%e prime(prime(3)) - prime(prime(2)) = 6. 6/2 = 3 = first term.

%e prime(prime(4)) - prime(prime(3)) = 6. 6/2 = 3 = second term.

%t With[{t = Table[Prime[Prime[n]], {n, 1, 400}]}, Select[(Rest[t] - Most[t])/2, PrimeQ]] (* _Amiram Eldar_, Jul 08 2024 *)

%o (PARI) lista(n) = for(x=1,n,y=prime(prime(x+1)) - prime(prime(x)); if(y%2==0&isprime(y/2),print1(y\2",")))

%Y Cf. A006450, A098042, A073131.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Sep 10 2004

%E Offset corrected by _Amiram Eldar_, Jul 08 2024