A056788 a(n) = n^n + (n-1)^(n-1).

2, 5, 31, 283, 3381, 49781, 870199, 17600759, 404197705, 10387420489, 295311670611, 9201412118867, 311791207040509, 11414881932150269, 449005897206417391, 18884637964090410991, 845687005960046315793

Offset

1,1

Comments

For even n > 1, the absolute value of the discriminant of the polynomial x^n+x-1. [Corrected by Artur Jasinski, May 07 2010]

The largest known prime in this sequence is a(4) = 283.

References

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see equation (6.7).

Links

Table of n, a(n) for n=1..17.

Walter Nissen, post on np ( n ) = n^n + (n+1)^(n+1), on home page "Up for the count!". (Updated Oct 02 2012)

Example

a(3) = 2^2 + 3^3 = 4 + 27 = 31.

Mathematica

Join[{2}, Table[n^n+(n-1)^(n-1), {n, 2, 20}]] (* T. D. Noe, Aug 13 2004 *)
Join[{2}, Total/@Partition[Table[n^n, {n, 20}], 2, 1]] (* Harvey P. Dale, Jun 26 2017 *)

Prog

(PARI) A056788(n)=n^n+(n-1)^(n-1)  \\ M. F. Hasler, Oct 02 2012

Crossrefs

Cf. A000312 (n^n), A086797 (discriminant of the polynomial x^n-x-1).

Cf. A056187, A056790, A192397 (smallest & largest prime factor of a(n), records of the latter), A217435 = bigomega(a(n)).

Sequence in context: A056790 A192397 A097396 * A091859 A085873 A303289

Adjacent sequences: A056785 A056786 A056787 * A056789 A056790 A056791

Keyword

nonn

Author

Walter Nissen, Aug 20 2000

Extensions

Minor corrections by M. F. Hasler, Oct 02 2012

Status

approved