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A082077
Balanced primes of order two.
22
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
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.
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 08 2003
STATUS
approved