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A037072 Squares which are the sum of twin prime pairs. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 15:16 EST 2022. Contains 350402 sequences. (Running on oeis4.)