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A082080 Smallest balanced prime of order n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..45.

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[{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)

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

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Last modified April 20 01:42 EDT 2014. Contains 240777 sequences.