A154675 Averages of twin prime pairs k such that k*13 and k/13 are squares.

1872, 7488, 11700, 825552, 990288, 1123668, 1629108, 3146832, 3302208, 4680000, 6627348, 7667712, 8783892, 15502032, 16017300, 16365492, 17252352, 25407252, 32617728, 42401268, 42966612, 54100800, 66163968, 71182800, 73019700

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Keywords

• nonn

Comments

Terms of this sequence must be of the form 13(6m)^2, the values for m are listed in A154775. - M. F. Hasler, Jan 15 2009

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A154670, A154671, A154672, A154673, A154674, A154775.

Programs

Mathematica

lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*13)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,11!,6}];lst
(* ... and/or ... *)
lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/13)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,11!,6}];lst
Select[13*Range[10^3]^2, And @@ PrimeQ[# + {-1, 1}] &] (* Amiram Eldar, Dec 25 2019 *)

PARI

for(i=1,499, isprime(468*i^2+1) && isprime(468*i^2-1) && print1(468*i^2",")) \\ M. F. Hasler, Jan 15 2009

Formula

a(n) = 468 A154775(n)^2 - M. F. Hasler, Jan 15 2009

Extensions

More terms from M. F. Hasler, Jan 15 2009