A082080 - OEIS

%I #25 Jul 12 2023 05:49:03

%S 2,5,79,17,491,53,71,29,37,983,5503,173,157,353,5297,263,179,383,137,

%T 2939,2083,751,353,5501,1523,149,4561,1259,397,787,8803,8803,607,227,

%U 3671,17443,57097,3607,23671,12539,1217,11087,1087,21407,19759,953

%N Smallest balanced prime of order n.

%C Or, smallest (2n+1)-balanced prime number.

%C 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).

%H Giovanni Resta, <a href="/A082080/b082080.txt">Table of n, a(n) for n = 0..10000</a> (first 1375 terms from Robert G. Wilson v)

%e a(1) = 5 = (3 + 5 + 7)/3 = 15/3.

%e a(5) = 53 = (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11 = 583/11.

%e a(6) = 71 = (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)/13 = 923/13.

%t f[n_] := Block[{p = Prime@ Range[2n +1]}, While[ Total[p] != (2n +1) p[[n +1]], p = Join[Rest@ p, {NextPrime[ p[[-1]]] }]]; p[[n +1]]]; Array[f, 46, 0] (* _Robert G. Wilson v_, Jun 21 2004 and modified Apr 11 2017 *)

%o (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 Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704.

%Y Cf. A006562, A051795, A081415, A096710, A055380, A082312, A075540, A054800.

%K nonn

%O 0,1

%A _Labos Elemer_, Apr 08 2003

%E Corrected and extended by _Ralf Stephan_, Apr 09 2003