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 A126554 Arithmetic mean of two consecutive balanced primes (of order one). 7
 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 (list; graph; refs; listen; history; text; internal format)
 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) FORMULA a(n) = (A006562(n+1)+A006562(n))/2. 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 Cf. A006562, A024675, A082077, A051795, A126555. Sequence in context: A142138 A341550 A009435 * A258721 A009406 A211496 Adjacent sequences: A126551 A126552 A126553 * A126555 A126556 A126557 KEYWORD nonn AUTHOR Artur Jasinski, Dec 27 2006 EXTENSIONS Edited by Klaus Brockhaus, Jan 05 2007 STATUS approved

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Last modified January 31 05:03 EST 2023. Contains 359947 sequences. (Running on oeis4.)