A357133 a(n) is the least prime that is the arithmetic mean of n consecutive primes.

5, 127, 79, 101, 17, 269, 491, 727, 53, 23, 71, 181, 29, 31, 37, 43, 563, 331, 883, 283, 173, 307, 157, 113, 353, 571, 347, 89, 263, 139, 179, 1201, 281, 1553, 137, 5167, 347, 563, 2083, 2087, 491, 1867, 353, 463, 1973, 199, 599, 4373, 149, 9929, 277, 463, 1259, 251, 397, 2897, 787, 263, 2161

Offset

3,1

Links

Robert Israel, Table of n, a(n) for n = 3..7000

Example

a(5) = 79 because 79 is the average of the 5 consecutive primes 71, 73, 79, 83, 89, and 79 is the least prime that works.

Maple

P:= [seq(ithprime(i), i=1..10^5)]:
S:= ListTools:-PartialSums(P):
g:= proc(n) local k, r;
   for k from 1 to 10^5-n do
      r:= (S[k+n]-S[k])/n;
      if r::integer and isprime(r) then return r fi
   od;
   -1
end proc:
map(g, [$3..100]);

Mathematica

a={}; n=3; For[k=1, k<=1200, k++, If[PrimeQ[p=Sum[Prime[k+i], {i, 0, n-1}]/n], AppendTo[a, p]; n++; k=1]]; a (* Stefano Spezia, Sep 15 2022 *)

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen():
    n, plst0 = 3, [2, 3, 5]
    while True:
        plst = plst0[:]
        while True:
            q, r = divmod(sum(plst), n)
            if r == 0 and isprime(q): yield q; break
            plst = plst[1:] + [nextprime(plst[-1])]
        plst0.append(nextprime(plst0[-1]))
        n += 1
print(list(islice(agen(), 60))) # Michael S. Branicky, Sep 14 2022

Crossrefs

Cf. A006562, A126096, A219478, A122531

Sequence in context: A015476 A059486 A071196 * A115233 A157438 A142803

Adjacent sequences: A357130 A357131 A357132 * A357134 A357135 A357136

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 14 2022

Status

approved