A082077 Balanced primes of order two.

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).

Subsequence of A219478, Peter Schorn, May 01 2025

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

Crossrefs

Cf. A006562, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704, A096693, A082080, A081415, A051795, A006562, A219478.

Sequence in context: A219505 A180455 A219478 * A389234 A341182 A158769

Adjacent sequences: A082074 A082075 A082076 * A082078 A082079 A082080

Keyword

nonn

Author

Labos Elemer, Apr 08 2003

Status

approved