A164130 Sums s of squares of three consecutive primes, such that s-+2 are primes.

195, 5739, 18459, 32259, 33939, 60291, 74019, 169491, 187131, 244899, 276819, 388179, 783531, 902139, 3588339, 5041491, 5145819, 5193051, 8687091, 9637491, 10227291, 10910019, 11341491, 11757339, 14834379, 15354651, 16115091

Offset

1,1

Links

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

Formula

A133529 INTERSECT A087679. - R. J. Mathar, Aug 27 2009

Example

5^2 + 7^2 + 11^2 = 195 is a sum of the squared consecutive primes 5, 7 and 11, and 193 and 197 are primes, so 195 is a member of the sequence.

Maple

q:= 2: r:= 3: R:= NULL: count:= 0:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  s:= p^2+q^2+r^2;
  if isprime(s-2) and isprime(s+2) then
    count:= count+1; R:= R, s;
  fi;
od:
R; # Robert Israel, Apr 21 2023

Mathematica

lst={}; Do[p=Prime[n]^2+Prime[n+1]^2+Prime[n+2]^2; If[PrimeQ[p-2]&&PrimeQ[p+2], AppendTo[lst, p]], {n, 8!}]; lst

Crossrefs

Cf. A075893, A133529, A133530, A034962, A164129

Sequence in context: A066232 A284960 A226105 * A084232 A145305 A174890

Adjacent sequences: A164127 A164128 A164129 * A164131 A164132 A164133

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 10 2009

Extensions

Comment turned into example by R. J. Mathar, Aug 27 2009

Status

approved