A082079 Balanced primes of order four.

491, 757, 1787, 3571, 6337, 6451, 6991, 7741, 7907, 8821, 10141, 10267, 10657, 12911, 15299, 16189, 18223, 18701, 19801, 19843, 19853, 19937, 21961, 22543, 22739, 22807, 23893, 23909, 24767, 25169, 25391, 26591, 26641, 26693, 26713

Offset: 1

Author

Labos Elemer, Apr 08 2003

Keywords

• nonn

Comments

The arithmetic mean of 8 primes in its "neighborhood"; not to be confused with 'Quadruply balanced primes' (A096710).

A balanced prime of order four is not necessarily balanced (A006562) order one, or of order two (A082077), or of order three (A082078), etc.

Examples

			p = 491 = (463 + 467 + 479 + 487 + 491 + 499 + 503 + 509 + 521)/9 = 4419/9.
		

Links

• Aaron Toponce, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006562, A082077, A082078, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704.

Cf. A096693, A082080, A081415, A051795, A006562.

Programs

GAP

P:=Filtered([1..50000],IsPrime);;
a:=List(Filtered(List([0..3000],k->List([5..13],j->P[j-4+k])), i-> Sum(i)/9=i[5]),m->m[5]); # Muniru A Asiru, Feb 14 2018

Mathematica

Do[s3=Prime[n]+Prime[n+1]+Prime[n+2]; s5=Prime[n-1]+s3+Prime[n+3]; s7=Prime[n-2]+s5+Prime[n+4]; s9=Prime[n-3]+s7+Prime[n+5]; If[Equal[s9/9, Prime[n+1]], Print[Prime[n+1]]], {n, 4, 10000}]
(* Second program: *)
With[{k = 4}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[3000], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]] (* Michael De Vlieger, Feb 15 2018 *)
Select[Partition[Prime[Range[3000]],9,1],Mean[#]==#[[5]]&][[;;,5]] (* Harvey P. Dale, Mar 09 2023 *)

PARI

isok(p) = {if (isprime(p), k = primepi(p); if (k > 4, sum(i=k-4, k+4, prime(i)) == 9*p;););} \\ Michel Marcus, Mar 07 2018