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.

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

Author

Zak Seidov, Oct 17 2002

Keywords

• easy
• nonn

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.

Examples

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

Crossrefs

Cf. A076815.

Programs

Mathematica

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

Formula

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

Extensions

More terms from Harvey P. Dale, May 22 2021