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A082077
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Balanced primes of order two.
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22
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79, 281, 349, 439, 643, 677, 787, 1171, 1733, 1811, 2141, 2347, 2389, 2767, 2791, 3323, 3329, 3529, 3929, 4157, 4349, 4751, 4799, 4919, 4951, 5003, 5189, 5323, 5347, 5521, 5857, 5861, 6287, 6337, 6473, 6967, 6997, 7507, 7933, 8233, 8377, 8429, 9377, 9623, 9629, 10093, 10333
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OFFSET
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1,1
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COMMENTS
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The arithmetic mean of 4 primes in its "neighborhood"; not to be confused with 'Doubly balanced primes' (A051795).
Balanced primes of order two are not necessarily balanced of order one (A006562) or three (A082078).
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LINKS
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EXAMPLE
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p = 79 = (71 + 73 + 79 + 83 + 89)/5 = 395/5 i.e. it is both the arithmetic mean and median.
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MATHEMATICA
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Do[s3=Prime[n]+Prime[n+1]+Prime[n+2]; s5=Prime[n-1]+s3+Prime[n+3]; If[Equal[s5/5, Prime[n+1]], Print[Prime[n+1]]], {n, 3, 3000}]
Select[Partition[Prime[Range[1500]], 5, 1], Mean[#]==#[[3]]&][[All, 3]] (* Harvey P. Dale, Nov 04 2019 *)
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PROG
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(PARI) p=2; q=3; r=5; s=7; forprime(t=11, 1e9, if(p+q+s+t==4*r, print1(r", ")); p=q; q=r; r=s; s=t) \\ Charles R Greathouse IV, Nov 20 2012
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CROSSREFS
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Cf. A006562, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704, A096693, A082080, A081415, A051795, A006562.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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