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A126554
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Arithmetic mean of two consecutive balanced primes (of order one).
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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
a(n) = (A006562(n+1)+A006562(n))/2.
For primes in this sequence (prime interprimes of order two) see A126555.
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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
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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
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CROSSREFS
| Cf. A006562, A024675, A082077, A051795, A126555.
Sequence in context: A069472 A142138 A009435 * A009406 A142176 A115272
Adjacent sequences: A126551 A126552 A126553 * A126555 A126556 A126557
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 27 2006
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 05 2007
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