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A082080 Smallest balanced prime of order n. 7
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).

Records: 2, 5, 79, 491, 983, 5503, 8803, 17443, 57097, 155219, 343583, 500179, 524521, 1208239, 1457969, 2076331, 2906291, 2977151, 3129031, 4893341, 8442079, 8560787, 11156987, 11596003, 14947939, 17922829, 20545477, 24597173, 25593493, 34395139, 34466101, etc. - Robert G. Wilson v, Apr 12 2017

LINKS

Robert G. Wilson v and 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

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Last modified July 21 08:37 EDT 2017. Contains 289638 sequences.