A076814 Integer averages of five successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2+prime(n+3)^2+prime(n+4)^2)/5, for some n (see A076814).

173329, 2723401, 7473769, 8941585, 9001465, 12978889, 13036537, 20273569, 36595345, 36682537, 52600465, 52774873, 52961113, 67138681, 67302601, 67473265, 78972121, 116515177, 121251433, 121560049, 123179113, 124184545, 124416361, 130951609, 141215449

Offset

1,1

Comments

Unlike the average of two, three or four successive primes squares, the average of five successive primes squared is not always an integer. The values of starting index in the sequence of five successive primes squared having integer average are in A076815.

Links

Table of n, a(n) for n=1..25.

Formula

(prime(n)^2+prime(n+1)^2+prime(n+2)^2+prime(n+3)^2+prime(n+4)^2)/5.

Example

173329 is OK because, starting with n=79, five successive primes squared has average 173329.

Mathematica

Select[Mean/@Partition[Prime[Range[2000]]^2, 5, 1], IntegerQ] (* Harvey P. Dale, May 22 2021 *)

Crossrefs

Cf. A076815.

Sequence in context: A233488 A233483 A251117 * A204792 A281621 A147314

Adjacent sequences: A076811 A076812 A076813 * A076815 A076816 A076817

Keyword

easy,nonn

Author

Zak Seidov, Oct 17 2002

Extensions

More terms from Harvey P. Dale, May 22 2021

Status

approved