A359394 Numbers k such that the average of the squares of k consecutive primes starting with 7 is a prime.

3, 4, 7, 9, 24, 28, 3872, 15172, 23440, 1390100, 7031920

Offset

1,1

Comments

a(12) > 2*10^8 if it exists.

Links

Table of n, a(n) for n=1..11.

Example

a(3) = 7 is a term because the average of the squares of the 7 consecutive primes starting with 7 is (7^2 + 11^2 + 13^2 + 17^2 + 19^2 + 23^2 + 29^2)/7 = 337, which is prime.

Maple

s:= 7^2: R:= NULL: count:= 0: p:= 7:
for n from 2 while count < 11 do
 p:= nextprime(p);
 s:= s + p^2;
 t:= s/n;
 if t::integer and isprime(t) then R:= R, n; count:= count+1 fi
od:
R;

Crossrefs

Cf. A359322.

Sequence in context: A221212 A218278 A101062 * A295399 A257507 A003669

Adjacent sequences: A359391 A359392 A359393 * A359395 A359396 A359397

Keyword

nonn,more

Author

Robert Israel, Dec 29 2022

Status

approved