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A126554
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Arithmetic mean of two consecutive balanced primes (of order one).
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7
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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