OFFSET
1,2
COMMENTS
Largest Katadrome (number with digits in strict descending order) in base n.
The largest permutational number (A134640) of order n. These numbers are isomorphic with antidiagonal permutation matrices of order n. Where diagonal matrices are a[i,1+n-i]=1 {i=1,n} a[i<>1+n-i]=0 for smallest permutational numbers of order n see A023811. - Artur Jasinski, Nov 07 2007
Permutational numbers A134640 isomorphic with permutation matrix generators of cyclic groups, n-th root of unity matrices. - Artur Jasinski, Nov 07 2007
Rephrasing: Largest pandigital number in base n (in the sense of A050278, which is base 10); e.g., a(10) = A050278(3265920), its final term. With a(1) = 1 instead of 0, also accommodates unary (A000042). - Rick L. Shepherd, Jul 10 2017
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..400
Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 1.
FORMULA
a(n) = n^n - (n^n-n)/(n-1)^2 for n>1. - Dean Hickerson, Jun 26 2001
MAPLE
0, seq(n*((n-2)*n^n + 1)/(n-1)^2, n=2..100); # Robert Israel, Sep 03 2014
MATHEMATICA
Table[Sum[i*n^i, {i, 0, -1 + n}], {n, 17}] (* Olivier Gérard, Jun 23 2001 *)
a[n_] := FromDigits[ Range[ n-1, 0, -1], n]; Array[a, 18] (* Robert G. Wilson v, Sep 03 2014 *)
PROG
(PARI) a(n) = sum(i=0, n-1, i*n^i)
(PARI) a(n) = if (n==1, 0, my(t=n^n); t-(t-n)/(n-1)^2); \\ Joerg Arndt, Sep 03 2014
(Haskell)
a062813 n = foldr (\dig val -> val * n + dig) 0 [0 .. n - 1]
-- Reinhard Zumkeller, Aug 29 2014
(Python)
def A062813(n): return (m:=n**n)-(m-n)//(n-1)**2 if n>1 else 0 # Chai Wah Wu, Mar 18 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Jun 23 2001
STATUS
approved