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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A299854 A154711 A162992 * A076432 A003848 A203753

Adjacent sequences: A037069 A037070 A037071 * A037073 A037074 A037075

Keyword

nonn

Author

G. L. Honaker, Jr.

Extensions

More terms from Amiram Eldar, Jan 01 2020

Status

approved