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A082078 Balanced primes of order three. 14
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

Table of n, a(n) for n=1..45.

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}]

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 A224269 A125637

Adjacent sequences:  A082075 A082076 A082077 * A082079 A082080 A082081

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 08 2003

STATUS

approved

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Last modified April 24 10:30 EDT 2014. Contains 240983 sequences.