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A082079 Balanced primes of order four. 15
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

Table of n, a(n) for n=1..35.

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}]

CROSSREFS

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

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

Sequence in context: A051115 A060975 A180457 * A217118 A205200 A205058

Adjacent sequences:  A082076 A082077 A082078 * A082080 A082081 A082082

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 08 2003

STATUS

approved

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Last modified July 28 00:26 EDT 2014. Contains 244987 sequences.