A131991 a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3.

15, 40, 156, 400, 1464, 2380, 5220, 7240, 12720, 25260, 30784, 52060, 70644, 81400, 106080, 151740, 208920, 230764, 305320, 363024, 394420, 499360, 578760, 712980, 922180, 1040604, 1103440, 1236600, 1307020, 1455780, 2064640, 2265384

Offset

1,1

Comments

Number of points and lines for the prime(n)-Cremona-Richmond configuration. - Carlos Segovia Gonzalez, Jul 30 2020

Links

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

C. Segovia and M. Winklmeier, Calculating the dimension of the universal embedding of the symplectic dual polar space using languages, arXiv:1312.4315 [math.CO], 2013-2019.

C. Segovia and M. Winklmeier, Calculating the dimension of the universal embedding of the symplectic dual polar space using languages, The Elec. Jour. of Comb. 27(4) (2020), P4.39.

Formula

a(n) = 1 + A060800(n)*A000040(n).

a(n) = (A030514(n) - 1)/A006093(n).

a(n) = A000203(A000040(n)^3). - Zak Seidov, Feb 13 2016

Example

a(4)=400 because the 4th prime is 7, 7^3=343, 7^2=49, and 343+49+7+1=400.

Maple

A131991:= n -> map (p -> p^(3)+p^(2)+p+1, ithprime(n)):
seq (A131991(n), n=1..32); # Jani Melik, Jan 25 2011

Mathematica

#^3 + #^2 + # + 1 &/@Prime[Range[100]] (* Vincenzo Librandi, Mar 20 2014 *)

Prog

(Magma) [1+NthPrime(n)+NthPrime(n)^2+NthPrime(n)^3: n in [1..40]]; // Vincenzo Librandi, Dec 27 2010

Crossrefs

Cf. A030078, A008864, A131992, A131993.

Cf. A000040, A000203. - Zak Seidov, Feb 13 2016

Sequence in context: A175926 A038991 A068020 * A116042 A219378 A280045

Adjacent sequences: A131988 A131989 A131990 * A131992 A131993 A131994

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 06 2007

Status

approved