A098043 Primes of the form (prime(prime(k+1)) - prime(prime(k)))/2.
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, 41, 31, 41, 11, 79, 7, 7, 23, 37, 31, 13, 29, 47, 13, 83, 29, 13, 11, 59, 17, 23, 17, 11, 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
Offset: 1
Examples
prime(prime(3)) - prime(prime(2)) = 6. 6/2 = 3 = first term. prime(prime(4)) - prime(prime(3)) = 6. 6/2 = 3 = second term.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
With[{t = Table[Prime[Prime[n]], {n, 1, 400}]}, Select[(Rest[t] - Most[t])/2, PrimeQ]] (* Amiram Eldar, Jul 08 2024 *) -
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",")))
Extensions
Offset corrected by Amiram Eldar, Jul 08 2024
Comments