A214451 - OEIS

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

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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);