A244092 Primes which are the arithmetic mean of two consecutive primes of the form 4n + 1.

23, 47, 67, 263, 563, 607, 647, 947, 1103, 1123, 1187, 1223, 1283, 1367, 1663, 1747, 1783, 1831, 1867, 1907, 2287, 2683, 2879, 2903, 2963, 3019, 3307, 3923, 4007, 4111, 4643, 5107, 5171, 5303, 5387, 5563, 5647, 5807, 6263, 6323, 6367, 6863, 7523, 7583, 7699

Offset

1,1

Comments

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

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A002144, A002145.

Sequence in context: A073025 A209193 A201019 * A042046 A042044 A042042

Adjacent sequences: A244089 A244090 A244091 * A244093 A244094 A244095

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 28 2014

Extensions

Several terms corrected or added by Colin Barker, Jun 28 2014

Status

approved