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 A082077 Balanced primes of order two. 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE p = 79 = (71 + 73 + 79 + 83 + 89)/5 = 395/5 i.e. it is both the arithmetic mean and median. MAPLE P:=proc(q) local n; for n from 3 to q do if (ithprime(n-2)+ithprime(n-1)+ithprime(n+1)+ithprime(n+2))/4=ithprime(n) then print(ithprime(n)); fi; od; end: P(10^6); # Paolo P. Lava, Mar 17 2014 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A006562, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704, A096693, A082080, A081415, A051795, A006562. Sequence in context: A219505 A180455 A219478 * A341182 A158769 A158774 Adjacent sequences:  A082074 A082075 A082076 * A082078 A082079 A082080 KEYWORD nonn AUTHOR Labos Elemer, Apr 08 2003 STATUS approved

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Last modified June 24 06:11 EDT 2021. Contains 345416 sequences. (Running on oeis4.)