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

1,1

Links

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

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 *)

Crossrefs

Cf. A154670, A154671, A154672.

Sequence in context: A272376 A288883 A206212 * A130179 A205756 A205586

Adjacent sequences: A154670 A154671 A154672 * A154674 A154675 A154676

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Status

approved