A082077 - OEIS

%I #33 Feb 23 2024 07:26:19

%S 79,281,349,439,643,677,787,1171,1733,1811,2141,2347,2389,2767,2791,

%T 3323,3329,3529,3929,4157,4349,4751,4799,4919,4951,5003,5189,5323,

%U 5347,5521,5857,5861,6287,6337,6473,6967,6997,7507,7933,8233,8377,8429,9377,9623,9629,10093,10333

%N Balanced primes of order two.

%C The arithmetic mean of 4 primes in its "neighborhood"; not to be confused with 'Doubly balanced primes' (A051795).

%C Balanced primes of order two are not necessarily balanced of order one (A006562) or three (A082078).

%H Charles R Greathouse IV, <a href="/A082077/b082077.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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}]

%t Select[Partition[Prime[Range[1500]],5,1],Mean[#]==#[[3]]&][[All,3]] (* _Harvey P. Dale_, Nov 04 2019 *)

%o (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

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

%K nonn

%O 1,1

%A _Labos Elemer_, Apr 08 2003