%I A082080
%S A082080 2,5,79,17,491,53,71,29,37,983,5503,173,157,353,5297,263,179,383,137,
%T A082080 2939,2083,751,353,5501,1523,149,4561,1259,397,787,8803,8803,607,227,
%U A082080 3671,17443,57097,3607,23671,12539,1217,11087,1087,21407,19759,953
%N A082080 Smallest balanced prime of order n.
%C A082080 Or, smallest (2n+1)-balanced prime number.
%C A082080 Prime(k) is a balanced prime of order n if it is the average of the 2n+1 
               primes from prime(k-n) to prime(k+n).
%e A082080 a(1) = 5 = (3 + 5 + 7)/3 = 15/3.
%e A082080 a(5) = 53 = (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11 
               = 583/11.
%e A082080 a(6) = 71 = (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 
               + 101)/13 = 923/13.
%t A082080 f[n_] := Block[{k = n + 2, s = Plus @@ Table[ Prime[i], {i, 2, 2n + 2}]}, 
               While[s != (2n + 1)Prime[k], k++; s = s - Prime[k - n - 1] + Prime[k 
               + n]]; Prime[k]]; Table[ f[n], {n, 47}] (from Robert G. Wilson v 
               Jun 21 2004)
%o A082080 (PARI) for(n=1,50,i=2*n+1:f=0:forprime(p=2,10^7,s=0:c=i:pr=p-1:t=0:while(c>
               0,c=c-1:pr=nextprime(pr+1):s=s+pr: if(c==(i-1)/2,t=pr)): if(s/i==t,
               print1(t","):f=1:break)): if(!f,print1("0,")))
%Y A082080 Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096699, 
               A096700, A096701, A096702, A096703, A096704.
%Y A082080 Cf. A006562, A051795, A081415, A096710, A055380, A082312, A075540, A054800.
%Y A082080 Sequence in context: A128297 A102983 A038583 this_sequence A127997 A096266 
               A123978
%Y A082080 Adjacent sequences: A082077 A082078 A082079 this_sequence A082081 A082082 
               A082083
%K A082080 nonn
%O A082080 0,1
%A A082080 Labos E. (labos(AT)ana.sote.hu), Apr 08 2003
%E A082080 Corrected and extended by Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 
               09 2003