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

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A037073.

Programs

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

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

Formula

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