A108231 a(n) = the first prime in the earliest sequence of 2n+1 consecutive primes whose average is prime.

3, 71, 7, 463, 31, 43, 5, 7, 499, 821, 109, 97, 271, 263, 179, 97, 181, 47, 233, 1931, 359, 227, 1787, 443, 29, 131, 1061, 229, 599, 1931, 7, 317, 53, 2207, 811, 11549, 2411, 2879, 5531, 937, 2371, 293, 21001, 659, 643, 1187, 2927, 4567, 131, 263, 8419, 349

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..5000

Example

71 is the first prime in the earliest sequence of 5 = 2 * 2 + 1 consecutive primes whose average is a prime, since (71 + 73 + 79 + 83 + 89)/5 = 79. Therefore a(2) = 71.

Maple

f:= proc(n) local L, i, s;
  L:= [seq(ithprime(i), i=1..2*n+1)]:
  s:= convert(L, `+`);
  do
    if s mod (2*n+1) = 0 and isprime(s/(2*n+1)) then return L[1] fi;
    s:= s - L[1];
    L:= [op(L[2..-1]), nextprime(L[-1])];
    s:= s + L[-1];
  od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 17 2025

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[ Sum[ Prime[j], {j, k, 2n + k}]/(2n + 1)], k++ ]; Prime[k]]; Table[ f[n], {n, 52}] (* Robert G. Wilson v, Jun 21 2005 *)
Module[{prs=Prime[Range[25000]]}, Table[SelectFirst[Partition[ prs, 2n+1, 1], PrimeQ[ Mean[ #]]&], {n, 60}]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 25 2017 *)

Crossrefs

Sequence in context: A135951 A361254 A093245 * A130894 A254665 A106894

Adjacent sequences: A108228 A108229 A108230 * A108232 A108233 A108234

Keyword

nonn

Author

Joseph L. Pe, Jun 16 2005

Extensions

More terms from Robert G. Wilson v, Jun 21 2005

Status

approved