A192397 -id:A192397 - cp's OEIS frontend

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, 40173648337182874339601, 2017766063735610126699403

Offset: 1

Walter Nissen, Aug 20 2000

nonn

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.

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

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

Pierre Letouzey, Generalized Hofstadter functions G, H and beyond: numeration systems and discrepancy, arXiv:2502.12615 [cs.DM], 2025. See p. 18.
Walter Nissen, post on np ( n ) = n^n + (n+1)^(n+1), on home page "Up for the count!". (Updated Oct 02 2012)

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)).

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 *)

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

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

A056790 Greatest prime factor of n^n + (n+1)^(n+1).

Original entry on oeis.org

2, 5, 31, 283, 23, 743, 331, 1600069, 410353, 60042893, 8969, 7438489991, 116803, 4879633159, 61215157711, 338142271, 34041259347101651, 45072130459, 6564253087266573169, 22022174223585405703, 121937899012999, 69454092876521107983605569601, 5311242856728321929909

Offset: 0

Walter Nissen, Aug 20 2000

Note that n^n + (n+1)^(n+1) = A056788(n+1).
Becomes "hard" (unknown) around n ~ 112, cf. link: As of today, even A217435(113) (number of prime factors) is unknown. - M. F. Hasler, Oct 04 2012
As of today, the first unknown term is a(143). - Daniel Suteu, Mar 11 2019

			a(4) = 23 because 4^4 + 5^5 = 3381 = 3 * 7^2 * 23.

Daniel Suteu, Table of n, a(n) for n = 0..142
Walter Nissen, np(n) = n^n + (n+1)^(n+1) -- 2 prominent questions. (Updated Oct 02 2012)

Cf. A056187, A192397.

Cf. A217435.

Join[{2},FactorInteger[Total[#]][[-1,1]]&/@Partition[Table[n^n,{n,30}],2,1]] (* Harvey P. Dale, Apr 21 2018 *)

A056790(n)=vecmax(factor((n+1)^(n+1)+n^n)[,1])  \\ M. F. Hasler, Oct 04 2012

a(n) = A006530(A056788(n+1)). - M. F. Hasler, Oct 04 2012

a(0) = 2 added by Arkadiusz Wesolowski, Jun 30 2011

a(21)-a(22) added by Daniel Suteu, Mar 11 2019

A056187 Least prime factor of n^n + (n+1)^(n+1).

Original entry on oeis.org

2, 5, 31, 283, 3, 67, 11, 11, 5, 173, 3, 1237, 7, 31, 7334881, 227, 3, 773, 149, 47, 11, 5, 3, 101, 13, 73, 151, 349, 3, 4421, 107, 191, 17, 7, 3, 17, 19, 624808693, 2273, 25788481, 3, 5, 59, 1752761753, 23, 2144707, 3, 49547, 5, 275851515609829434269, 19, 919, 3, 13, 7, 107, 29

Offset: 0

Walter Nissen, Aug 20 2000

nonn

			a(5) = 67 because 5^5 + 6^6 = 3125 + 46656 = 67 * 743.

Hugo Pfoertner, Table of n, a(n) for n = 0..234, (first 96 terms from Chai Wah Wu).
factordb.com, Status of 235^235+236^236.
Walter Nissen, np(n) = n^n + (n+1)^(n+1) -- 2 prominent questions. (Updated Oct 02 2012)

Cf. A056788, A056790, A192397, A217435.

A056187(n)=factor((n+1)^(n+1)+n^n)[1,1] \\ M. F. Hasler, Oct 04 2012

a(n) = A020639(A056788(n+1)). - M. F. Hasler, Oct 04 2012

2 added by Arkadiusz Wesolowski, Jun 30 2011

a(53)-a(56) from Chai Wah Wu, Jul 22 2019

cp's OEIS Frontend

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

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A056790 Greatest prime factor of n^n + (n+1)^(n+1).

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A056187 Least prime factor of n^n + (n+1)^(n+1).

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