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 A082078 Balanced primes of order three. 17
 17, 53, 157, 173, 193, 229, 349, 439, 607, 659, 701, 709, 977, 1153, 1187, 1301, 1619, 2281, 2287, 2293, 2671, 2819, 2843, 3067, 3313, 3539, 3673, 3727, 3833, 4013, 4051, 4517, 4951, 5101, 5897, 6079, 6203, 6211, 6323, 6679, 6869, 7321, 7589, 7643, 7907 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The arithmetic mean of 6 primes in its "neighborhood"; not to be confused with 'Triply balanced primes' (A081415). A balanced prime of order three is not necessarily balanced of order one (A006562) or two (A082077), etc. [Typo corrected by Zak Seidov, Jul 23 2008] LINKS Aaron Toponce, Table of n, a(n) for n = 1..1000 EXAMPLE p = 53 = (41 + 43 + 47 + 53 + 59 + 61 + 67)/7 = 371/7 i.e. it is the arithmetic mean. MAPLE P:=proc(q) local n; for n from 3 to q do if (ithprime(n-3)+ithprime(n-2)+ithprime(n-1)+ithprime(n+1)+ ithprime(n+2)+ithprime(n+3))/6 = 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]; If[Equal[s7/7, Prime[n+1]], Print[Prime[n+1]]], {n, 3, 5000}] (* Second program: *) With[{k = 3}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[10^3], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]]  (* Michael De Vlieger, Feb 15 2018 *) PROG (GAP) P:=Filtered([1..10000], IsPrime);; a:=List(Filtered(List([0..1000], k->List([4..10], j->P[j-3+k])), i-> Sum(i)/7=i[4]), m->m[4]); # Muniru A Asiru, Feb 14 2018 (PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 3, sum(i=k-3, k+3, prime(i)) == 7*p; ); ); } \\ Michel Marcus, Mar 07 2018 CROSSREFS Cf. A006562, A082077, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704. Cf. A096693, A082080, A081415, A051795, A006562. Sequence in context: A180456 A154409 A033213 * A107175 A244270 A244271 Adjacent sequences:  A082075 A082076 A082077 * A082079 A082080 A082081 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.)