A152787 Numbers k such that both k and k^2/2 are averages of twin prime pairs.

6, 12, 42, 72, 600, 642, 882, 2130, 2382, 2688, 3558, 3582, 4548, 6132, 7548, 8010, 9042, 13398, 13932, 15972, 17598, 19140, 21492, 26250, 26262, 34512, 38670, 39228, 39342, 48312, 49740, 52542, 53088, 53592, 55050, 55662, 56100, 56712, 65028, 65448, 65520

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 12 2008

Keywords

• nonn

Links

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

Crossrefs

Cf. A014574, A152786.

Programs

Magma

[2*k:k in [1..40000]| IsPrime(2*k-1) and IsPrime(2*k+1) and IsPrime(2*k^2 -1) and IsPrime(2*k^2 +1) ]; // Marius A. Burtea, Dec 31 2019

Mathematica

lst={};Do[p1=Prime[n];p2=Prime[n+1];If[p2-p1==2,e=(2*(p1+1))^(1/2);i=Floor[e]; If[e==i,If[PrimeQ[i-1]&&PrimeQ[i+1],AppendTo[lst,i]]]],{n,10!}];lst
Select[Mean/@Select[Partition[Prime[Range[10000]],2,1],#[[2]]-#[[1]] == 2&],And@@PrimeQ[#^2/2+{1,-1}]&](* Harvey P. Dale, May 12 2014 *)

Formula

A152786 INTERSECT A014574. - R. J. Mathar, Jan 08 2009

Extensions

Rephrased definition by R. J. Mathar, Jan 08 2009

More terms from Harvey P. Dale, May 12 2014