A069487 Areas of Pythagorean triangles (A069482, A069484, A069486).

30, 240, 840, 5544, 6864, 26520, 23256, 73416, 208104, 107880, 467976, 473304, 296184, 727560, 1494600, 2101344, 863760, 3138816, 2625864, 1492704, 5259504, 4248936, 7623384, 12845904, 7759224, 4244424

Offset

1,1

Links

Marius A. Burtea, Table of n, a(n) for n = 1..5000

César Aguilera, Two Prime Number Objects and The Velucchi Numbers, hal-02909691 [math.NT], 2020.

Formula

a(n) = A030078(n+1)*A000040(n) - A000040(n+1)*A030078(n).

a(n) = A000040(n+1)^3*A000040(n) - A000040(n+1)*A000040(n)^3.

a(n) = A000040(n)*A127917(n+1) - A127917(n)*A000040(n+1). - César Aguilera, Sep 18 2019

Example

prime(2)^3 * prime(1) - prime(1)^3 * prime(2) = 3^3 * 2 - 2^3 * 3 = 54 - 24 = 30 that is the area of the Pythagorean triangle (5, 12, 13), so a(1) = 30. - Bernard Schott, Sep 23 2019

Prog

(Magma) [NthPrime(n+1)^3*NthPrime(n)-NthPrime(n+1)*(NthPrime(n)^3):n in [1..26]]; // Marius A. Burtea, Sep 19 2019

Crossrefs

Cf. A069482, A069484, A069486.

Cf. A000040, A030078, A127917.

Sequence in context: A339750 A196412 A081779 * A008385 A061167 A189495

Adjacent sequences: A069484 A069485 A069486 * A069488 A069489 A069490

Keyword

nonn

Author

Reinhard Zumkeller, Mar 29 2002

Status

approved