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 A051795 Doubly balanced primes: primes which are averages of both their immediate and their second neighbors. 15
 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 (list; graph; refs; listen; history; text; internal format)
 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 3-balanced=A006562;[3,5,7]-balanced=A081415. - Labos Elemer, Apr 02 2003 LINKS Jud McCranie and Sebastian Petzelberger, Table of n, a(n) for n = 1..10000 (first 1000 terms from Jud McCranie) 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(n-1)+ithprime(n+1))/2=ithprime(n) and (ithprime(n-2)+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[n-1]+Prime[n]+Prime[n+1]; s1=Prime[n-2]+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 Cf. A006562, A081415, A096710, A055380. Sequence in context: A267028 A226150 A081416 * A338949 A269886 A269765 Adjacent sequences: A051792 A051793 A051794 * A051796 A051797 A051798 KEYWORD easy,nonn AUTHOR Harvey P. Dale, Dec 10 1999 STATUS approved

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Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)