A076815 -id:A076815 - cp's OEIS frontend

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

Zak Seidov, Oct 17 2002

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.

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

Cf. A076815.

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

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

More terms from Harvey P. Dale, May 22 2021

A288376 Primes of the form k!2+2, where k!2 is the double factorial number (A006852).

Original entry on oeis.org

3, 5, 17, 107, 947, 13749310577, 316234143227, 213458046676877, 495179769008019818390136611716089140627, 13114900840751548972796135496384318234575359262373046877, 28352254429826839019508359891905756542124154226667992913078222750278633810791015627

Offset: 1

Robert Price, Jun 08 2017

nonn

Robert Price, Table of n, a(n) for n = 1..12
Henri& Renaud Lifchitz, PRP Records.Search for n!2+2.
Joe McLean, Interesting Sources of Probable Primes
OpenPFGW Project, Primality Tester

Cf. A076815.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 2] + 2, {i, 0, 100}], PrimeQ[#]&]

cp's OEIS Frontend

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.

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