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 A127922 1/24 of product of three numbers: n-th prime, previous and following number. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 *) 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

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Last modified August 12 03:18 EDT 2020. Contains 336436 sequences. (Running on oeis4.)