A234370 Primes which are the arithmetic mean of the squares of five consecutive primes.

2723401, 13036537, 52774873, 78972121, 116515177, 123179113, 235236049, 242120017, 834990721, 850037521, 943067353, 943804801, 1302156313, 1582432681, 1659047497, 1830419449, 1999538809, 2025774697, 2609800657

Offset: 1

Author

K. D. Bajpai, Dec 25 2013

Keywords

• nonn

Examples

			2723401 is in the sequence because (1627^2 + 1637^2 + 1657^2 + 1663^2 + 1667^2)/5 = 2723401 which is prime.
52774873 is in the sequence because (7243^2 + 7247^2 + 7253^2 + 7283^2 + 7297^2)/5 = 52774873 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3270

Crossrefs

Cf. A084951: primes of the form (prime(k)^2 + prime(k+1)^2 + prime(k+2)^2)/3.

Cf. A093343: primes of the form (prime(k)^2 + prime(k+1)^2)/2.

Programs

Maple

KD := proc() local a,b,d,e,f,g; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=ithprime(n+3); f:=ithprime(n+4); g:=(a^2+b^2+d^2+e^2+f^2)/5; if g=floor(g) and isprime(g) then RETURN (g); fi; end: seq(KD(), n=1..10000);

Mathematica

Select[Mean/@Partition[Prime[Range[6000]]^2,5,1],PrimeQ] (* Harvey P. Dale, Aug 01 2020 *)