A051442 a(n) = n^(n+1)+(n+1)^n.

1, 3, 17, 145, 1649, 23401, 397585, 7861953, 177264449, 4486784401, 125937424601, 3881436747409, 130291290501553, 4731091158953433, 184761021583202849, 7721329860319737601, 343809097055019694337, 16248996011806421522977

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Odd prime p divides a(p-2). For n>1, a(prime(n)-2)/prime(n) = A125074(n) = {1, 29, 3343, 407889491, 298572057493, 454195874136455153, ...}. Prime p divides a((p+5)/2) for p = {19, 23, 61}. - Alexander Adamchuk, Nov 18 2006

From Mathew Englander, Jul 08 2020: (Start)

For all n != 1, a(n) mod 8 = 1.

If n mod 6 = 0, 3, or 5, then a(n) mod 6 = 1. If n mod 6 = 1, then a(n) mod 6 = 3. If n mod 6 = 2 or 4, then a(n) mod 6 = 5.

For all n, a(n)-1 is a multiple of n^2.

For n odd and n >= 3, a(n)-1 is a multiple of (n+1)^2.

For n even and n >= 0, a(n)+1 is a multiple of (n+1)^2.

For proofs, see the Englander link. (End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Mathew Englander, Notes on OEIS A051442

Crossrefs

Cf. A007925, A051443, A125074, A076980, A173054, A208506.

Programs

Magma

[n^(n+1)+(n+1)^n: n in [0..20]]; // Vincenzo Librandi, Jan 12 2012

Mathematica

Table[n^(n+1)+(n+1)^n,{n,0,20}] (* Harvey P. Dale, Oct 02 2018 *)

Maxima

A051442[n]:=n^(n+1)+(n+1)^n$ makelist(A051442[n],n,0,30); /* Martin Ettl, Oct 29 2012 */

PARI

a(n)=(n+1)^n+n^(n+1) \\ Charles R Greathouse IV, Jan 12 2012

Formula

a(n) = (n + e + o(1)) * n^n. - Charles R Greathouse IV, Jan 12 2012

From Mathew Englander, Jul 08 2020: (Start)

a(n) = A093898(n+1, n) for n >= 1.

a(n) = a(n-1) + A258389(n) for n >= 1.

a(n) = A007778(n) + A000169(n+1).

(End)