A143682 - OEIS

%I #18 Sep 08 2022 08:45:37

%S 7,14,103,391,5002,8967,31065,45724,107077,301276,382000,820141,

%T 1246909,1479730,2129740,3534420,5523879,6237871,9209731,11625564,

%U 12865129,17844972,21754756,28999632,41437737,48684207,52341667,60941856

%N a(n) = (prime(n)^4 - prime(n^4))/2, where prime(n) is the n-th prime.

%H G. C. Greubel, <a href="/A143682/b143682.txt">Table of n, a(n) for n = 1..750</a>

%e a(1) = (prime(1)^2^2 - prime(1^2^2))/2 = (16 - 2)/2 = 14/2 = 7,

%e a(2) = (prime(2)^2^2 - prime(2^2^2))/2 = (81 - 53)/2 = 28/2 = 14,

%e a(3) = (prime(3)^2^2 - prime(3^2^2))/2 = (625 - 419)/2 = 206/2 = 103,

%e a(4) = (prime(4)^2^2 - prime(4^2^2))/2 = (2401 - 1619)/2 = 782/2 = 391 = a(4),

%e a(5) = (prime(5)^2^2 - prime(5^2^2))/2 = (14641 - 4637)/2 = 10004/2 = 5002,

%e etc.

%p A143682 := proc(n) (ithprime(n)^4-ithprime(n^4))/2 ; end: for n from 1 to 50 do printf("%d,",A143682(n)) ; od: # _R. J. Mathar_, Nov 05 2008

%t Table[(Prime[n]^4 - Prime[n^4])/2, {n, 40}] (* _G. C. Greubel_, May 29 2021 *)

%o (PARI) a(n) = (prime(n)^4 - prime(n^4))/2; \\ _Michel Marcus_, Oct 05 2015

%o (Magma) [(NthPrime(n)^4 - NthPrime(n^4))/2: n in [1..30]]; // _Vincenzo Librandi_, Oct 05 2015

%o (Sage) [(nth_prime(n)^4 - nth_prime(n^4))/2 for n in (1..40)] # _G. C. Greubel_, May 29 2021

%Y Cf. A000040.

%Y Cf. A030514, A109791. - _R. J. Mathar_, Nov 05 2008

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 01 2008

%E More terms from _R. J. Mathar_, Nov 05 2008