

A051795


Doubly balanced primes: primes which are averages of both their immediate and their second neighbors.


16



18731, 25621, 28069, 30059, 31051, 44741, 76913, 97441, 103669, 106681, 118831, 128449, 135089, 182549, 202999, 240491, 245771, 249199, 267569, 295387, 347329, 372751, 381401, 435751, 451337, 455419, 471521, 478099, 498301, 516877, 526441
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OFFSET

1,1


COMMENTS

Could also be called overbalanced or [3,5]balanced primes: balanced primes which are equally average of 3,5 consecutive prime neighbors as follows: a(n)=[q+a(n)+r]/3=[p+q+a(n)+r+s]/5 See 3balanced=A006562;[3,5,7]balanced=A081415.  Labos Elemer, Apr 02 2003


LINKS



EXAMPLE

25621 belongs to the sequence because 25621 = (25609 + 25633)/2 = (25603 + 25609 + 25633 + 25639)/4.


MAPLE

P:=proc(q) local n; for n from 3 to q do
if (ithprime(n1)+ithprime(n+1))/2=ithprime(n) and (ithprime(n2)+ithprime(n+2))/2=ithprime(n) then print(ithprime(n)); fi; od; end: P(10^6); # Paolo P. Lava, Mar 17 2014


MATHEMATICA

Do[s=Prime[n1]+Prime[n]+Prime[n+1]; s1=Prime[n2]+s+Prime[n+2]; If[Equal[s/3, Prime[n]]&&Equal[s1/5, Prime[n]], Print[Prime[n]]], {n, 4, 1000000}] (* Labos Elemer *)
Transpose[Select[Partition[Prime[Range[50000]], 5, 1], (#[[1]]+#[[5]])/2 == (#[[2]]+#[[4]])/2 == #[[3]]&]][[3]] (* Harvey P. Dale, Sep 13 2013 *)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



