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

Author

Alex Ratushnyak, Jul 18 2012

Keywords

• nonn

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

Examples

			(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.
		

Links

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

Crossrefs

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

Programs

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