OFFSET
1,1
COMMENTS
Might be called interprimes of order two, since the arithmetic means of two consecutive odd primes (A024675) sometimes are called interprimes.
Balanced primes of order two (A082077) and doubly balanced primes (A051795) have different definitions.
For primes in this sequence (prime interprimes of order two) see A126555.
LINKS
Muniru A Asiru and Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Muniru A Asiru)
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, 1000}]; Do[AppendTo[b, (a[[k + 1]] + a[[k]])/2], {k, 1, Length[a] - 1}]; b
PROG
(PARI) {m=6000; a=0; p=2; q=3; r=5; while(r<=m, if((p+r)/2==q, if(a>0, print1((a+q)/2, ", ")); a=q); p=q; q=r; r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 05 2007
(GAP) P:=Filtered([1..6000], IsPrime);; P1:=List(Filtered(List([0..Length(P)-3], k->List([1..3], j->P[j+k])), i->Sum(i)/3=i[2]), m->m[2]);;
a:=List([1..Length(P1)-1], n->(P1[n+1]+P1[n])/2); # Muniru A Asiru, Mar 31 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 27 2006
EXTENSIONS
Edited by Klaus Brockhaus, Jan 05 2007
STATUS
approved