login
A069487
Areas of Pythagorean triangles (A069482, A069484, A069486).
4
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 29 2002
STATUS
approved