A122531 -id:A122531 - cp's OEIS frontend

A122040 Numbers which are equal to the arithmetic mean of six successive primes.

12, 15, 22, 26, 30, 34, 38, 42, 55, 64, 77, 82, 87, 92, 101, 105, 110, 115, 126, 139, 144, 160, 165, 170, 190, 227, 232, 274, 279, 292, 298, 304, 312, 326, 339, 346, 352, 358, 369, 375, 387, 393, 406, 413, 419, 431, 436, 442, 447, 452, 469, 481, 516, 524, 533

Offset: 1

Giovanni Teofilatto, Sep 14 2006

			a(1) = 12 because (5+7+11+13+17+19)/6 = 12;
a(2) = 15 because (7+11+13+17+19+23)/6 = 15.

Cf. A122531.

Select[Table[Sum[Prime[k], {k, n, n + 5}]/6, {n, 100}], IntegerQ] (* Ray Chandler, Sep 25 2006 *)
Select[Mean/@Partition[Prime[Range[200]],6,1],IntegerQ]  (* Harvey P. Dale, Apr 01 2011 *)

Extended by Ray Chandler, Sep 25 2006

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

Original entry on oeis.org

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

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

nonn

			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.

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

Cf. A006562, A126096, A219478, A122531

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]);

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 *)

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

cp's OEIS Frontend

A122040 Numbers which are equal to the arithmetic mean of six successive primes.

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