OFFSET
1,2
COMMENTS
Also smallest pandigital number in base n. - Franklin T. Adams-Watters, Nov 15 2006
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
Eric Weisstein's World of Mathematics, Pandigital Number
Wikipedia, Pandigital number
Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 1.
FORMULA
a(n) = (102345....n-1) in base n. - Ulrich Schimke (ulrschimke(AT)aol.com)
For n > 1, a(n) = (n^n-n)/(n-1)^2 + n^(n-2)*(n-1) - 1 = A023811(n) + A053506(n). - Franklin T. Adams-Watters, Nov 15 2006
a(n) = n^(n-1) + Sum_{m=2..n-1} m * n^(n - 1 - m). - Alexander R. Povolotsky, Sep 18 2022
EXAMPLE
a(6) = 102345_6 = 1*6^5 + 2*6^3 + 3*6^2 + 4*6^1 + 5*6^0 = 8345.
MAPLE
a:= n-> n^(n-1)+add((n-i)*n^(i-1), i=1..n-2):
seq(a(n), n=1..23); # Alois P. Heinz, May 02 2020
MATHEMATICA
Table[FromDigits[Join[{1, 0}, Range[2, n-1]], n], {n, 20}] (* Harvey P. Dale, Oct 12 2012 *)
PROG
(PARI) A049363(n)=n^(n-1)+sum(i=1, n-2, n^(i-1)*(n-i)) \\ M. F. Hasler, Jan 10 2012
(PARI) A049363(n)=if(n>1, (n^n-n)/(n-1)^2+n^(n-2)*(n-1)-1, 1) \\ M. F. Hasler, Jan 12 2012
(Haskell)
a049363 n = foldl (\v d -> n * v + d) 0 (1 : 0 : [2..n-1])
-- Reinhard Zumkeller, Apr 04 2012
(Python)
def A049363(n): return (n**n-n)//(n-1)**2+n**(n-2)*(n-1)-1 if n>1 else 1 # Chai Wah Wu, Mar 13 2024
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
EXTENSIONS
More terms from Ulrich Schimke (ulrschimke(AT)aol.com)
STATUS
approved