A093898 -id:A093898 - cp's OEIS frontend

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

N. J. A. Sloane

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)

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

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

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

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

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

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

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)

A160814 a(1) = 1; a(n+1) = a(n)^n + n^a(n).

Original entry on oeis.org

1, 2, 8, 7073

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 26 2009

nonn

Next term is too large to display: 2.3459495195697547514*10^4258

The next term (a(5)) has 4259 digits. - Harvey P. Dale, Jul 18 2021

Cf. A093898, A055652, A076980. - R. J. Mathar, May 29 2009

a=1;lst={};Do[a=a^n+n^a;AppendTo[lst,IntegerPart[a]],{n,0,4}];lst
nxt[{n_, a_}] := {n + 1, a^n + n^a}; NestList[nxt, {1, 1}, 4][[All, 2]] (* Harvey P. Dale, Jul 18 2021 *)

Edited by N. J. A. Sloane, May 29 2009

cp's OEIS Frontend

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

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