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A082078
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Balanced primes of order three.
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18
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17, 53, 157, 173, 193, 229, 349, 439, 607, 659, 701, 709, 977, 1153, 1187, 1301, 1619, 2281, 2287, 2293, 2671, 2819, 2843, 3067, 3313, 3539, 3673, 3727, 3833, 4013, 4051, 4517, 4951, 5101, 5897, 6079, 6203, 6211, 6323, 6679, 6869, 7321, 7589, 7643, 7907
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OFFSET
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1,1
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COMMENTS
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The arithmetic mean of 6 primes in its "neighborhood"; not to be confused with 'Triply balanced primes' (A081415).
A balanced prime of order three is not necessarily balanced of order one (A006562) or two (A082077), etc. [Typo corrected by Zak Seidov, Jul 23 2008]
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LINKS
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EXAMPLE
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p = 53 = (41 + 43 + 47 + 53 + 59 + 61 + 67)/7 = 371/7 i.e. it is the arithmetic mean.
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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]; s7=Prime[n-2]+s5+Prime[n+4]; If[Equal[s7/7, Prime[n+1]], Print[Prime[n+1]]], {n, 3, 5000}]
(* Second program: *)
With[{k = 3}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[10^3], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]] (* Michael De Vlieger, Feb 15 2018 *)
Select[Partition[Prime[Range[1500]], 7, 1], Mean[#]==#[[4]]&][[All, 4]] (* Harvey P. Dale, Jul 01 2022 *)
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PROG
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(GAP) P:=Filtered([1..10000], IsPrime);;
a:=List(Filtered(List([0..1000], k->List([4..10], j->P[j-3+k])), i->
(PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 3, sum(i=k-3, k+3, prime(i)) == 7*p; ); ); } \\ Michel Marcus, Mar 07 2018
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CROSSREFS
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Cf. A006562, A082077, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704.
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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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