A214451 Arithmetic mean of next a(n) successive squares of positive integers is prime.

5, 11, 29, 43, 17, 131, 13, 7, 17, 7, 53, 19, 25, 35, 65, 59, 17, 35, 113, 43, 25, 35, 5, 7, 5, 11, 89, 23, 17, 35, 29, 43, 5, 31, 109, 71, 65, 7, 41, 31, 61, 35, 25, 107, 25, 11, 41, 47, 25, 175, 41, 35, 29, 23, 17, 43, 197, 91, 13, 95, 17, 47, 5, 7, 25, 11

Offset

1,1

Comments

Corresponding primes (arithmetic means) :

11, 131, 1031, 4643, 9433, 30671, 59063, 64013, 70249, 76733, 94483, 117679, 133277, 156127, 198377, 257339, 297049, 326143, 417089, 522883, 573101, 619471, 651251, 660973, 670763

All terms are in A007310. Do all members of A007310 except 1 occur? - Robert Israel, May 02 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

(1+4+9+16+25)/5 = 11, so a(1)=5. The next set of successive squares with prime arithmetic mean: (6^2 + 7^2 + ... + 16^2)/11=131, so a(2)=11.

Maple

r:= 0:
for n from 1 to 100 do
  t:= 0:
  for j from r+1 do
    t:= t + j^2;
    s:= t/(j-r);
    if s::integer and isprime(s) then
      A[n]:= j-r;
      r:= j;
      break
    fi
  od;
od:
seq(A[i], i=1..100); # Robert Israel, May 02 2018

Crossrefs

Cf. A000040, A000290, A007310, A214442, A214444.

Sequence in context: A074367 A088486 A174917 * A340544 A062772 A319597

Adjacent sequences: A214448 A214449 A214450 * A214452 A214453 A214454

Keyword

nonn

Author

Alex Ratushnyak, Jul 18 2012

Status

approved