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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

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

Sequence in context: A060975 A180457 A271664 * A260925 A217118 A205200

Adjacent sequences: A082076 A082077 A082078 * A082080 A082081 A082082

Keyword

nonn

Author

Labos Elemer, Apr 08 2003

Status

approved