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A154673 Averages of twin prime pairs k such that k*7 and k/7 are squares. 6
2268, 6300, 30492, 49392, 81648, 100800, 170352, 183708, 197568, 211932, 242172, 363888, 444528, 681408, 847728, 1032192, 1342908, 1694448, 1820700, 2041200, 3049200 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 19 06:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)