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 A154673 Averages of twin prime pairs k such that k*7 and k/7 are squares. 6

%I

%S 2268,6300,30492,49392,81648,100800,170352,183708,197568,211932,

%T 242172,363888,444528,681408,847728,1032192,1342908,1694448,1820700,

%U 2041200,3049200

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

%H Amiram Eldar, <a href="/A154673/b154673.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..100 from Harvey P. Dale)

%t 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

%t 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 *)

%t Select[7*Range[10^3]^2, And @@ PrimeQ[# + {-1, 1}] &] (* _Amiram Eldar_, Dec 25 2019 *)

%Y Cf. A154670, A154671, A154672.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009

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Last modified May 18 10:28 EDT 2022. Contains 353807 sequences. (Running on oeis4.)