OFFSET
2,3
COMMENTS
The first two terms of the series illustrate the famous equalities 3^2 + 4^2 = 5^2 and 3^3 + 4^3 + 5^3 = 6^3. The following terms show how this eventually diverges.
LINKS
Wikipedia, Number 143
FORMULA
a(n) = (n+3)^n - Sum_{k=3..n+2} k^n.
a(n) ~ k*n^n, where k = e^3/(e-1). - Charles R Greathouse IV, Oct 08 2012
MAPLE
a:= n-> (n+3)^n -add(k^n, k=3..n+2):
seq (a(n), n=2..20); # Alois P. Heinz, Oct 08 2012
MATHEMATICA
a[n_] := (n+3)^n + 2^n - HarmonicNumber[n+2, -n] + 1; Table[a[n], {n, 2, 20}] (* Jean-François Alcover, Feb 17 2014 *)
Table[(n+3)^n-Total[Range[3, n+2]^n], {n, 2, 20}] (* Harvey P. Dale, Sep 22 2019 *)
PROG
(PARI) a(n)=(n+3)^n-sum(k=3, n+2, k^n) \\ Charles R Greathouse IV, Oct 08 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Beaudoin, Oct 05 2012
STATUS
approved