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

Author

Labos Elemer, Apr 08 2003

Keywords

• nonn

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

Examples

			p = 79 = (71 + 73 + 79 + 83 + 89)/5 = 395/5 i.e. it is both the arithmetic mean and median.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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 *)

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