A008788 -id:A008788 - cp's OEIS frontend

A262067 a(n) = n^n - (n-2)^n.

2, 4, 26, 240, 2882, 42560, 745418, 15097600, 347066882, 8926258176, 253930611002, 7916100448256, 268352394448322, 9828088361009152, 386707997366768618, 16268790735900180480, 728714136550643404802, 34624041592426892361728

Offset: 1

Altug Alkan, Sep 10 2015

Inspired by multi-dimensional cubes: For n>1, the number of lattice points on the surface of a k-dimensional cube with side-length n is f(n,k) = n^k - (n-2)^k. a(n) = f(n,n).

			For n = 2, a(n) = n^n - (n-2)^n = 2^2 - (2-2)^2 = 4.

Cf. A000312, A008788.

For sequences with "Number of points on surface of k-dimensional cube," cf. A130130 (k=1), A008574 (k=2, shifted), A005897 (k=3), A008511 (k=4), A008512 (k=5), A008513 (k=6).

[n^n - (n-2)^n : n in [1..20]]; // Wesley Ivan Hurt, Sep 10 2015

A262067:=n->n^n - (n-2)^n: seq(A262067(n), n=1..20); # Wesley Ivan Hurt, Sep 10 2015

Array[#^# - (# - 2)^# &, {18}] (* Michael De Vlieger, Sep 10 2015 *)

a(n) = n^n - (n-2)^n;
vector(40, n, a(n))

a(n) = A000312(n) - A008788(n-2).

A279884 a(n) = (prime(n)-1)^(prime(n)+1) + 1.

Original entry on oeis.org

2, 17, 4097, 1679617, 1000000000001, 1283918464548865, 4722366482869645213697, 12748236216396078174437377, 165251092644282265779977014214657, 25986090120790645892257018950637850957185025, 185302018885184100000000000000000000000000000001

Offset: 1

Jaroslav Krizek, Dec 23 2016

nonn

Prime terms are in A279883.
Subsequence of {A008788(n) + 1}.
Conjecture: If (n-1)^(n+1) + 1 is a prime, then n = prime.

			For n=3; a(3) = (prime(3)-1)^(prime(3)+1) + 1 = 4^6 + 1 = 4097.

Cf. A000040, A279883.

[(NthPrime(n)-1)^(NthPrime(n)+1)+1: n in[1..50]]

Table[(# - 1)^(# + 1) + 1 &[Prime@ n], {n, 11}] (* Michael De Vlieger, Dec 23 2016 *)

a(n) = (prime(n)-1)^(prime(n)+1)+1 \\ Felix Fröhlich, Dec 23 2016

A316295 Decimal expansion of x such that x^(x+2) = x^x + x^2.

Original entry on oeis.org

1, 4, 9, 1, 7, 7, 9, 7, 0, 9, 3, 3, 2, 8, 4, 9, 8, 4, 1, 2, 5, 2, 3, 2, 8, 3, 3, 8, 7, 4, 6, 5, 8, 9, 7, 7, 3, 5, 3, 5, 5, 9, 5, 3, 0, 2, 7, 2, 5, 6, 8, 8, 2, 0, 8, 2, 5, 8, 1, 5, 5, 4, 3, 7, 6, 7, 7, 9, 7, 7, 6, 4, 8, 2, 2, 8, 3, 9, 0, 0, 2, 0, 4, 4, 8, 9, 0, 4, 1, 6, 8, 8, 0, 3, 4, 5, 8, 4, 6, 9, 7, 6, 1, 6, 7

Offset: 1

Patrick C. Schneider, Jun 29 2018

			1.4917797093328498412523283387465897735355953027256882082581554376779776...

Cf. A008788 (x^(x+2)).

RealDigits[ NSolve[x^(x + 2) == x^x + x^2, x, Reals, WorkingPrecision -> 128][[1, 1, 2]], 10][[1]] (* Robert G. Wilson v, Jul 21 2018 *)

PARI
```
solve(x=1, 2, x^(x+2)-x^x-x^2)
```

A090650 n^(n+6).

Original entry on oeis.org

1, 256, 19683, 1048576, 48828125, 2176782336, 96889010407, 4398046511104, 205891132094649, 10000000000000000, 505447028499293771, 26623333280885243904, 1461920290375446110677, 83668255425284801560576

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Dec 13 2003

nonn

Cf. A000312, A007778, A008788, A008789, A008790, A008791.

a:=n->mul(n,k=-5..n):seq(a(n),n=1..14); # Zerinvary Lajos, Jan 26 2008

Table[n^(n+6),{n,0,40}](* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

cp's OEIS Frontend

A262067 a(n) = n^n - (n-2)^n.

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A279884 a(n) = (prime(n)-1)^(prime(n)+1) + 1.

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A316295 Decimal expansion of x such that x^(x+2) = x^x + x^2.

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Examples

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Mathematica

PARI

A090650 n^(n+6).

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Maple

Mathematica