A084952 Middle q of three consecutive primes p,q,r such that (p^2 + q^2 + r^2)/3 is prime.

11, 13, 23, 43, 53, 103, 211, 223, 233, 263, 271, 281, 293, 317, 331, 349, 397, 431, 463, 479, 499, 557, 577, 643, 761, 773, 787, 797, 829, 929, 1187, 1327, 1373, 1399, 1427, 1429, 1451, 1453, 1483, 1583, 1627, 1667, 1693, 1747, 1753, 1783, 2027, 2099, 2129

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3)=23 because (19^2 + 23^2 + 29^2)/3 = 1731/3 = 577 is prime.

Maple

q:= 5: r:= 7:
Res:= NULL: count:= 0:
while count < 100 do
  p:= q;
  q:= r;
  r:= nextprime(r);
  if isprime((p^2+q^2+r^2)/3) then count:= count+1; Res:= Res, q fi
od:
Res; # Robert Israel, Aug 20 2018

Mathematica

Select[Partition[Prime[Range[400]], 3, 1], PrimeQ[Total[#^2]/3]&][[;; , 2]] (* Harvey P. Dale, Sep 08 2023 *)

Crossrefs

Cf. A075893, A084951.

Sequence in context: A097933 A166484 A127043 * A277048 A275598 A090433

Adjacent sequences: A084949 A084950 A084951 * A084953 A084954 A084955

Keyword

easy,nonn

Author

Hugo Pfoertner, Jun 14 2003

Status

approved