A037072 Squares which are the sum of twin prime pairs.

36, 144, 1764, 2304, 5184, 7056, 8100, 30276, 41616, 69696, 93636, 138384, 166464, 207936, 224676, 298116, 352836, 360000, 412164, 562500, 725904, 777924, 876096, 944784, 956484, 1077444, 1299600, 1468944, 1617984, 1920996, 2160900, 2286144, 2304324, 2509056

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn

Comments

There are exactly 5^2 squares less than or equal to 1000^2 which are the sum of twin prime pairs.

Examples

			36 (square) = 6^2 = 17 + 19 (twin prime pair).
		

Links

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

Crossrefs

Cf. A000290, A001359, A006512, A152786, A154670.

Programs

Magma

[k^2:k in [2..1700 by 2]| IsPrime(k^2 div 2 -1) and IsPrime(k^2 div 2 +1)]; // Marius A. Burtea, Jan 01 2020

Mathematica

lst={};Do[p=n^2;If[PrimeQ[p/2-1]&&PrimeQ[p/2+1], AppendTo[lst, p]], {n, 0, 7!, 2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)

Formula

a(n) = 2 * A154670(n) = A152786(n)^2. - Amiram Eldar, Jan 01 2020

Extensions

More terms from Amiram Eldar, Jan 01 2020