

A127922


1/24 of product of three numbers: nth prime, previous and following number.


4



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
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OFFSET

2,2


COMMENTS

The product of (n1), n, and (n+1) = n^3  n.  Harvey P. Dale, Jan 17 2011
For n > 2, a(n) = A001318(n2) * A007310(n1), if A007310(n1) 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^21)/2 and the hypotenuse to have a side length of (p^2+1)/2. The resulting triangle has an area equal to (p1)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


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 *)


PROG

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


CROSSREFS

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



