A127922 1/24 of product of three numbers: n-th prime, previous and following number.

1, 5, 14, 55, 91, 204, 285, 506, 1015, 1240, 2109, 2870, 3311, 4324, 6201, 8555, 9455, 12529, 14910, 16206, 20540, 23821, 29370, 38024, 42925, 45526, 51039, 53955, 60116, 85344, 93665, 107134, 111895, 137825, 143450, 161239, 180441, 194054

Offset

2,2

Comments

The product of (n-1), n, and (n+1) = n^3 - n. - Harvey P. Dale, Jan 17 2011

For n > 2, a(n) = A001318(n-2) * A007310(n-1), if A007310(n-1) is prime. Also a(n) is a subsequence of A000330. - Richard R. Forberg, Dec 25 2013

If p is an odd prime it can always be the side length of a leg of a primitive Pythagorean triangle. However it constrains the other leg to have a side length of (p^2-1)/2 and the hypotenuse to have a side length of (p^2+1)/2. The resulting triangle has an area equal to (p-1)*p*(p+1)/4. a(n) is 1/6 the area of such triangles. - Frank M Jackson, Dec 06 2017

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

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

Formula

a(n) = A011842(A000040(n) + 1) = A000330((A000040(n) - 1) / 2).

Mathematica

Table[(Prime[n] + 1) Prime[n](Prime[n] - 1)/24, {n, 1, 100}] (#^3-#)/ 24&/@ Prime[Range[2, 40]] (* Harvey P. Dale, Jan 17 2011 *)
((#-1)#(#+1))/24&/@Prime[Range[2, 40]] (* Harvey P. Dale, Jan 20 2023 *)

Prog

(PARI) for(n=2, 25, print1((prime(n)+1)*prime(n)*(prime(n)-1)/24, ", ")) \\ G. C. Greubel, Jun 19 2017

Crossrefs

Cf. A000040, A000330, A011842.

Cf. A036689, A034953, A127917, A127918, A127919, A127920, A127921, A011842.

Sequence in context: A268887 A055488 A177049 * A262247 A279511 A281698

Adjacent sequences: A127919 A127920 A127921 * A127923 A127924 A127925

Keyword

nonn

Author

Artur Jasinski, Feb 06 2007

Status

approved