A133063 - OEIS

%I #18 Oct 08 2024 13:10:36

%S 176,1278,15950,84966,809006,1862718,7113446,12400350,32217158,

%T 102627230,143233206,346869006,579484406,735277038,1147032086,

%U 2091418478,3575230670,4223655006,6751518846,9022210406,10366514358,15386748630,19696904798,27922396310,42939420486,52553573006

%N a(n) = 5*p^5 + 3*p^3 - 2*p^2, where p = prime(n).

%H G. C. Greubel, <a href="/A133063/b133063.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 5*(p(n))^5 + 3*(p(n))^3 - 2*(p(n))^2, where p(n)=A000040(n).

%e a(4)=84966 because the 4th prime is 7, 5*7^5=84035, 3*7^3=1029, 2*7^2=98 and we can write 84035+1029-98=84966.

%p a:= n-> (p-> (5*p^3+3*p-2)*p^2)(ithprime(n)):

%p seq(a(n), n=1..26);  # _Alois P. Heinz_, Sep 23 2024

%t Table[(Prime[n])^2*(5*Prime[n]^3 + 3*Prime[n] - 2), {n, 1, 50}] (* _G. C. Greubel_, Oct 09 2017 *)

%o (Magma) [5*p^5+3*p^3-2*p^2: p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Dec 15 2010

%o (PARI) for(n=1,25, print1(5*prime(n)^5 + 3*prime(n)^3 - 2*prime(n)^2, ", ")) \\ _G. C. Greubel_, Oct 09 2017

%Y Cf. A000290, A000578, A000584, A045991, A133072. Prime numbers: A000040.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Nov 05 2007

%E More terms from _Vincenzo Librandi_, Dec 15 2010