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A082077 Balanced primes of order two. 19
79, 281, 349, 439, 643, 677, 787, 1171, 1733, 1811, 2141, 2347, 2389, 2767, 2791, 3323, 3329, 3529, 3929, 4157, 4349, 4751, 4799, 4919, 4951, 5003, 5189, 5323, 5347, 5521, 5857, 5861, 6287, 6337, 6473, 6967, 6997, 7507, 7933, 8233, 8377, 8429, 9377, 9623, 9629, 10093, 10333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The arithmetic mean of 4 primes in its "neighborhood"; not to be confused with 'Doubly balanced primes' (A051795).

Balanced primes of order two are not necessarily balanced of order one (A006562) or three (A082078) .

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

p = 79 = (71 + 73 + 79 + 83 + 89)/5 = 395/5 i.e. it is both the arithmetic mean and mode.

MAPLE

P:=proc(q) local n; for n from 3 to q do

if (ithprime(n-2)+ithprime(n-1)+ithprime(n+1)+ithprime(n+2))/4=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]; If[Equal[s5/5, Prime[n+1]], Print[Prime[n+1]]], {n, 3, 3000}]

PROG

(PARI) p=2; q=3; r=5; s=7; forprime(t=11, 1e9, if(p+q+s+t==4*r, print1(r", ")); p=q; q=r; r=s; s=t) \\ Charles R Greathouse IV, Nov 20 2012

CROSSREFS

Cf. A006562, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704, A096693, A082080, A081415, A051795, A006562.

Sequence in context: A219505 A180455 A219478 * A158769 A158774 A157507

Adjacent sequences:  A082074 A082075 A082076 * A082078 A082079 A082080

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 08 2003

STATUS

approved

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Last modified October 24 16:46 EDT 2014. Contains 248516 sequences.