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A143682 a(n) = (prime(n)^4 - prime(n^4))/2, where prime(n) is the n-th prime.

%I A143682 #18 Sep 08 2022 08:45:37
%S A143682 7,14,103,391,5002,8967,31065,45724,107077,301276,382000,820141,
%T A143682 1246909,1479730,2129740,3534420,5523879,6237871,9209731,11625564,
%U A143682 12865129,17844972,21754756,28999632,41437737,48684207,52341667,60941856
%N A143682 a(n) = (prime(n)^4 - prime(n^4))/2, where prime(n) is the n-th prime.
%H A143682 G. C. Greubel, <a href="/A143682/b143682.txt">Table of n, a(n) for n = 1..750</a>
%e A143682 a(1) = (prime(1)^2^2 - prime(1^2^2))/2 = (16 - 2)/2 = 14/2 = 7,
%e A143682 a(2) = (prime(2)^2^2 - prime(2^2^2))/2 = (81 - 53)/2 = 28/2 = 14,
%e A143682 a(3) = (prime(3)^2^2 - prime(3^2^2))/2 = (625 - 419)/2 = 206/2 = 103,
%e A143682 a(4) = (prime(4)^2^2 - prime(4^2^2))/2 = (2401 - 1619)/2 = 782/2 = 391 = a(4),
%e A143682 a(5) = (prime(5)^2^2 - prime(5^2^2))/2 = (14641 - 4637)/2 = 10004/2 = 5002,
%e A143682 etc.
%p A143682 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 A143682 Table[(Prime[n]^4 - Prime[n^4])/2, {n, 40}] (* _G. C. Greubel_, May 29 2021 *)
%o A143682 (PARI) a(n) = (prime(n)^4 - prime(n^4))/2; \\ _Michel Marcus_, Oct 05 2015
%o A143682 (Magma) [(NthPrime(n)^4 - NthPrime(n^4))/2: n in [1..30]]; // _Vincenzo Librandi_, Oct 05 2015
%o A143682 (Sage) [(nth_prime(n)^4 - nth_prime(n^4))/2 for n in (1..40)] # _G. C. Greubel_, May 29 2021
%Y A143682 Cf. A000040.
%Y A143682 Cf. A030514, A109791. - _R. J. Mathar_, Nov 05 2008
%K A143682 nonn
%O A143682 1,1
%A A143682 _Juri-Stepan Gerasimov_, Nov 01 2008
%E A143682 More terms from _R. J. Mathar_, Nov 05 2008