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

1,1

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A232040 A054817 A270244 * A068281 A139668 A244019

Adjacent sequences: A154672 A154673 A154674 * A154676 A154677 A154678

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Extensions

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

Status

approved