A154673 Averages of twin prime pairs k such that k*7 and k/7 are squares.

2268, 6300, 30492, 49392, 81648, 100800, 170352, 183708, 197568, 211932, 242172, 363888, 444528, 681408, 847728, 1032192, 1342908, 1694448, 1820700, 2041200, 3049200

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Harvey P. Dale)

Crossrefs

Cf. A154670, A154671, A154672.

Programs

Mathematica

lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*7)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst...and/or... lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/7)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst
Select[Mean/@Select[Partition[Prime[Range[250000]],2,1],#[[2]]-#[[1]] == 2&],AllTrue[{Sqrt[7#],Sqrt[#/7]},IntegerQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 22 2018 *)
Select[7*Range[10^3]^2, And @@ PrimeQ[# + {-1, 1}] &] (* Amiram Eldar, Dec 25 2019 *)