A244092 - OEIS

%I #30 Aug 18 2014 08:11:46

%S 23,47,67,263,563,607,647,947,1103,1123,1187,1223,1283,1367,1663,1747,

%T 1783,1831,1867,1907,2287,2683,2879,2903,2963,3019,3307,3923,4007,

%U 4111,4643,5107,5171,5303,5387,5563,5647,5807,6263,6323,6367,6863,7523,7583,7699

%N Primes which are the arithmetic mean of two consecutive primes of the form 4n + 1.

%C All terms must necessarily be primes of the form 4n+3.

%H Jens Kruse Andersen, <a href="/A244092/b244092.txt">Table of n, a(n) for n = 1..10000</a>

%e 23 is in this sequence because (A002144(3) + A002144(4))/2 = (17 + 29)/2 = 23 and 23 is prime.

%t pythagPrimes = Select[4Range[500] + 1, PrimeQ]; len = Length[pythagPrimes]; pythagPrimeMeans = Table[(pythagPrimes[[n]] + pythagPrimes[[n + 1]])/2, {n, len - 1}]; Select[pythagPrimeMeans, PrimeQ] (* _Alonso del Arte_, Jul 12 2014 *)

%o (PARI)

%o p=[]; forstep(n=1, 8000, 4, if(isprime(n), p=concat(p, n))); p;

%o s=[]; for(k=1, #p-1, if(isprime(q=(p[k]+p[k+1])\2), s=concat(s, q))); s \\ _Colin Barker_, Jun 28 2014

%Y Cf. A002144, A002145.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jun 28 2014

%E Several terms corrected or added by _Colin Barker_, Jun 28 2014