This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160501 #15 Jun 25 2021 23:14:48
%S A160501 9,251,16627,48844509,13109522141,232643574681223,144347818589843079,
%T A160501 8863082234840576951801,100000008862938119652501095929,
%U A160501 192043424957750480504146841291811
%N A160501 (n+1)^prime(n+1) + n^prime(n).
%C A160501 a(2)=251 is the only prime found for n up to 10000 using The C/Gmp program in the link which is 17 times faster than the PARI routine.
%C A160501 Here there are divisibility rules: If prime(n) and prime(n+1) do not differ by 6, then n^2+n+1 is a divisor. So finding primes in this case will be difficult since 5/6 of the numbers are composite at the onset.
%C A160501 If another prime exists, it is larger than 418977 digits.
%H A160501 Harvey P. Dale, <a href="/A160501/b160501.txt">Table of n, a(n) for n = 1..95</a>
%H A160501 C. L. Hilliard,<a href="http://groups.google.com/group/prime-index-powers/web/c-gmp-prime-indices-to-prime-power">Sum of prime indices to respective primes</a>
%F A160501 a(n) = (n+1)^prime(n+1) + n^prime(n) = A062481(n)+A062481(n+1).
%e A160501 For n = 3, 4^7 + 3^5 = 16627, the 3rd entry in the sequence.
%t A160501 Table[n^Prime[n]+(n+1)^Prime[n+1],{n,10}] (* _Harvey P. Dale_, Sep 10 2016 *)
%t A160501 Total/@Partition[Table[n^Prime[n] ,{n,15}],2,1] (* _Harvey P. Dale_, Sep 22 2020 *)
%o A160501 (PARI) ppower(n) = { for(x=1,n, y=(x+1)^prime(x+1) + x^prime(x); print1(y", ") ); }
%Y A160501 Cf. A160491.
%K A160501 nonn
%O A160501 1,1
%A A160501 _Cino Hilliard_, May 15 2009
%E A160501 Edited by _R. J. Mathar_, May 30 2009