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A082079
Balanced primes of order four.
19
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 08 2003
STATUS
approved