A154670 Averages of twin prime pairs k such that k*2 and k/2 are squares.

18, 72, 882, 1152, 2592, 3528, 4050, 15138, 20808, 34848, 46818, 69192, 83232, 103968, 112338, 149058, 176418, 180000, 206082, 281250, 362952, 388962, 438048, 472392, 478242, 538722, 649800, 734472, 808992, 960498, 1080450, 1143072

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = 18*A037073(n)^2. - M. F. Hasler, Jan 15 2009

Example

18/2 = 9 = 3^2, 18*2 = 36 = 6^2.

Mathematica

lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1], s=Sqrt[n*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=Sqrt[n/2]; If[Floor[s]==s, AppendTo[lst, n]]], {n, 6, 10!, 6}]; lst

Prog

(PARI) for(i=1, 999, isprime(18*i^2+1) && isprime(18*i^2-1) && print1(18*i^2", ")) \\ M. F. Hasler, Jan 15 2009

Crossrefs

Cf. A037073.

Sequence in context: A007276 A052619 A110753 * A394757 A394399 A041626

Adjacent sequences: A154667 A154668 A154669 * A154671 A154672 A154673

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Status

approved