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a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3.
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%I #43 Sep 08 2022 08:45:31

%S 15,40,156,400,1464,2380,5220,7240,12720,25260,30784,52060,70644,

%T 81400,106080,151740,208920,230764,305320,363024,394420,499360,578760,

%U 712980,922180,1040604,1103440,1236600,1307020,1455780,2064640,2265384

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

%C Number of points and lines for the prime(n)-Cremona-Richmond configuration. - _Carlos Segovia Gonzalez_, Jul 30 2020

%H Vincenzo Librandi, <a href="/A131991/b131991.txt">Table of n, a(n) for n = 1..1000</a>

%H C. Segovia and M. Winklmeier, <a href="https://arxiv.org/abs/1312.4315">Calculating the dimension of the universal embedding of the symplectic dual polar space using languages</a>, arXiv:1312.4315 [math.CO], 2013-2019.

%H C. Segovia and M. Winklmeier, <a href="https://doi.org/10.37236/9754">Calculating the dimension of the universal embedding of the symplectic dual polar space using languages</a>, The Elec. Jour. of Comb. 27(4) (2020), P4.39.

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

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

%F a(n) = A000203(A000040(n)^3). - _Zak Seidov_, Feb 13 2016

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

%p A131991:= n -> map (p -> p^(3)+p^(2)+p+1, ithprime(n)):

%p seq (A131991(n), n=1..32); # _Jani Melik_, Jan 25 2011

%t #^3 + #^2 + # + 1 &/@Prime[Range[100]] (* _Vincenzo Librandi_, Mar 20 2014 *)

%o (Magma) [1+NthPrime(n)+NthPrime(n)^2+NthPrime(n)^3: n in [1..40]]; // _Vincenzo Librandi_, Dec 27 2010

%Y Cf. A030078, A008864, A131992, A131993.

%Y Cf. A000040, A000203. - _Zak Seidov_, Feb 13 2016

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Aug 06 2007