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 A082079 Balanced primes of order four. 18
 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 (list; graph; refs; listen; history; text; internal format)
 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. MAPLE P:=proc(q) local n; for n from 3 to q do if (ithprime(n-4)+ithprime(n-3)+ithprime(n-2)+ithprime(n-1)+ithprime(n+1)+ ithprime(n+2)+ithprime(n+3)+ ithprime(n+4))/8 = ithprime(n) then print(ithprime(n)); fi; od; end: P(10^6); # Paolo P. Lava, Mar 17 2014 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 *) 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

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Last modified May 26 11:30 EDT 2022. Contains 354086 sequences. (Running on oeis4.)