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

1,1

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A014574, A152786.

Sequence in context: A267309 A206039 A048069 * A060551 A129113 A377119

Adjacent sequences: A152784 A152785 A152786 * A152788 A152789 A152790

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 12 2008

Extensions

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

More terms from Harvey P. Dale, May 12 2014

Status

approved