A127918 Half of product of three numbers: n-th prime, previous and following number.

3, 12, 60, 168, 660, 1092, 2448, 3420, 6072, 12180, 14880, 25308, 34440, 39732, 51888, 74412, 102660, 113460, 150348, 178920, 194472, 246480, 285852, 352440, 456288, 515100, 546312, 612468, 647460, 721392, 1024128, 1123980, 1285608

Offset

1,1

Comments

Apart from the first term, the same as A117762. - R. J. Mathar, Jun 14 2008

Except the first term, a(n) is the area of the integer-sided isosceles triangle ABC with AB=AC such that the altitude AH is of prime(n) length.

The couples (a(n), altitude) are (12,3), (60,5), (168,7), (660,11), (1092,13), ... and the sequence of the ratio a(n)/prime(n) is {4, 12, 24, 60, 84, 144, 180, ...} - see A084921. - Michel Lagneau, Oct 23 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

Table[(Prime[n] + 1) Prime[n](Prime[n] - 1)/2, {n, 1, 100}]

Prog

(PARI) forprime(p=2, 1e3, print1(3*binomial(p+1, 3)", ")) \\ Charles R Greathouse IV, Jun 16 2011
(Magma) [(NthPrime(n)+1)*NthPrime(n)*(NthPrime(n)-1)/2: n in [1..40]]; // Vincenzo Librandi, Apr 09 2017

Crossrefs

Cf. A036689, A034953, A127917, A127920.

Sequence in context: A114419 A090830 A233283 * A069944 A253171 A073996

Adjacent sequences: A127915 A127916 A127917 * A127919 A127920 A127921

Keyword

nonn,easy

Author

Artur Jasinski, Feb 06 2007

Status

approved