A126555 Primes in A126554.

29, 1439, 4211, 7703, 12907, 14957, 16703, 20947, 29221, 31189, 33053, 36749, 44531, 51437, 90247, 115547, 124783, 127163, 133337, 144511, 146449, 151339, 157133, 166219, 169241, 180233, 181031, 185123, 197383, 223367, 225287, 240347

Offset: 1

Author

Artur Jasinski, Dec 27 2006

Keywords

• nonn

Comments

Primes that are the arithmetic mean of two consecutive balanced primes (of order one); primes of the form (A006562(k)+A006562(k+1))/2.

Might be called prime interprimes of order two.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A126554, A006562.

Programs

Mathematica

b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1,10000}];Do[If[PrimeQ[(a[[k + 1]] + a[[k]])/2], AppendTo[b, (a[[k + 1]] + a[[k]])/2]], {k, 1, Length[a] - 1}]; b

PARI

{m=250000;a=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,if(isprime(b=(a+q)/2),print1(b,",")));a=q);p=q;q=r;r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 05 2007

Extensions

Edited and extended by Klaus Brockhaus, Jan 05 2007