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

1,1

Links

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

Example

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.

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 *)

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.

Sequence in context: A081409 A251997 A104848 * A051384 A251350 A238070

Adjacent sequences: A234367 A234368 A234369 * A234371 A234372 A234373

Keyword

nonn

Author

K. D. Bajpai, Dec 25 2013

Status

approved