A160491 -id:A160491 - cp's OEIS frontend

A160501 (n+1)^prime(n+1) + n^prime(n).

9, 251, 16627, 48844509, 13109522141, 232643574681223, 144347818589843079, 8863082234840576951801, 100000008862938119652501095929, 192043424957750480504146841291811

Offset: 1

Cino Hilliard, May 15 2009

nonn

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.
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.
If another prime exists, it is larger than 418977 digits.

			For n = 3, 4^7 + 3^5 = 16627, the 3rd entry in the sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..95
C. L. Hilliard,Sum of prime indices to respective primes

Cf. A160491.

Table[n^Prime[n]+(n+1)^Prime[n+1],{n,10}] (* Harvey P. Dale, Sep 10 2016 *)
Total/@Partition[Table[n^Prime[n] ,{n,15}],2,1] (* Harvey P. Dale, Sep 22 2020 *)

ppower(n) = { for(x=1,n, y=(x+1)^prime(x+1) + x^prime(x); print1(y", ") ); }

a(n) = (n+1)^prime(n+1) + n^prime(n) = A062481(n)+A062481(n+1).

Edited by R. J. Mathar, May 30 2009

cp's OEIS Frontend

A160501 (n+1)^prime(n+1) + n^prime(n).

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