A126554 Arithmetic mean of two consecutive balanced primes (of order one).

29, 105, 165, 192, 234, 260, 318, 468, 578, 600, 630, 693, 840, 962, 1040, 1113, 1155, 1205, 1295, 1439, 1629, 1750, 1830, 2097, 2352, 2547, 2790, 2933, 3135, 3310, 3475, 3685, 3873, 4211, 4433, 4527, 4627, 4674, 4842, 5050, 5110, 5208, 5345, 5390, 5478

Offset: 1

Author

Artur Jasinski, Dec 27 2006

Keywords

• nonn

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)

Crossrefs

Cf. A006562, A024675, A082077, A051795, A126555.

Programs

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

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

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

Formula

a(n) = (A006562(n+1)+A006562(n))/2.

Extensions

Edited by Klaus Brockhaus, Jan 05 2007