A082080 Smallest balanced prime of order n.

2, 5, 79, 17, 491, 53, 71, 29, 37, 983, 5503, 173, 157, 353, 5297, 263, 179, 383, 137, 2939, 2083, 751, 353, 5501, 1523, 149, 4561, 1259, 397, 787, 8803, 8803, 607, 227, 3671, 17443, 57097, 3607, 23671, 12539, 1217, 11087, 1087, 21407, 19759, 953

Offset

0,1

Comments

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

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).

Links

Giovanni Resta, Table of n, a(n) for n = 0..10000 (first 1375 terms from Robert G. Wilson v)

Example

a(1) = 5 = (3 + 5 + 7)/3 = 15/3.
a(5) = 53 = (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11 = 583/11.
a(6) = 71 = (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)/13 = 923/13.

Mathematica

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 *)

Prog

(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, ")))

Crossrefs

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

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

Sequence in context: A216847 A102983 A038583 * A127997 A096266 A123978

Adjacent sequences: A082077 A082078 A082079 * A082081 A082082 A082083

Keyword

nonn

Author

Labos Elemer, Apr 08 2003

Extensions

Corrected and extended by Ralf Stephan, Apr 09 2003

Status

approved