A234364 Primes which are the arithmetic mean of the squares of four consecutive primes.

157, 337, 673, 1213, 1777, 2137, 11677, 20773, 27259, 32803, 80407, 84787, 89227, 105397, 120097, 165313, 176461, 181513, 250543, 417337, 453667, 463807, 576883, 610867, 791317, 804757, 853873, 935167, 949687, 1087903

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..5666

Example

157 is in the sequence because (7^2 + 11^2 + 13^2 + 17^2)/4 = 157 which is prime.
1213 is in the sequence because (29^2 + 31^2 + 37^2 + 41^2)/4 = 1213 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); g:=(a^2+b^2+d^2+e^2)/4; if g=floor(g) and isprime(g) then RETURN (g);  fi;  end: seq(KD(), n=1..500);

Mathematica

Select[Table[Mean[Prime[Range[n, n + 3]]^2], {n, 250}], PrimeQ] (* Alonso del Arte, Dec 26 2013 *)
Select[Mean/@(Partition[Prime[Range[200]], 4, 1]^2), PrimeQ] (* Harvey P. Dale, Oct 08 2014 *)

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: A140625 A142874 A346431 * A060974 A073277 A180233

Adjacent sequences: A234361 A234362 A234363 * A234365 A234366 A234367

Keyword

nonn

Author

K. D. Bajpai, Dec 25 2013

Status

approved