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

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

Offset

1,1

Comments

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..95

C. L. Hilliard,Sum of prime indices to respective primes

Formula

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

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A160491.

Sequence in context: A007408 A066989 A249593 * A075987 A135099 A073427

Adjacent sequences: A160498 A160499 A160500 * A160502 A160503 A160504

Keyword

nonn

Author

Cino Hilliard, May 15 2009

Extensions

Edited by R. J. Mathar, May 30 2009

Status

approved