OFFSET
1,3
COMMENTS
Also smallest zeroless pandigital number in base n. - Franklin T. Adams-Watters, Nov 15 2006
The smallest permutational number in A134640 in the n-positional system. - Artur Jasinski, Nov 07 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Christian Perfect, Integer sequence reviews on Numberphile (or vice versa), 2013.
Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 1.
FORMULA
a(n) = Sum_{j=1...n-1} j*n^(n-1-j).
lim_{n->infinity} a(n)/a(n-1) - a(n-1)/a(n-2) = exp(1). - Conjectured by Gerald McGarvey, Sep 26 2004. Follows from the formula below and lim_{n->infinity} (1+1/n)^n = e. - Franklin T. Adams-Watters, Jan 25 2010
a(n) = (n^n-n^2+n-1)/(n-1)^2 = A058128(n)-1 = n*A060073(n)-1 (for n>=2). - Henry Bottomley, Feb 21 2001
EXAMPLE
a(5) = 1234[5] (in base 5) = 1*5^3 + 2*5^2 + 3*5 + 4 = 125 + 50 + 15 + 4 = 194.
a(10) = 123456789 (in base 10).
MAPLE
0, seq((n^n-n^2+n-1)/(n-1)^2, n=2..100); # Robert Israel, Dec 13 2015
MATHEMATICA
Table[Total[(#1 n^#2) & @@@ Transpose@ {Range[n - 1], Reverse@ (Range[n - 1] - 1)}], {n, 20}] (* Michael De Vlieger, Jul 24 2015 *)
Table[Sum[(b - k)*b^(k - 1), {k, b - 1}], {b, 30}] (* Clark Kimberling, Aug 22 2015 *)
Table[FromDigits[Range[0, n - 1], n], {n, 20}] (* L. Edson Jeffery, Dec 13 2015 *)
PROG
(PARI) {for(i=1, 18, cuo=0; for(j=1, i-1, cuo=cuo+j*i^(i-j-1)); print1(cuo, ", "))} \\\ Douglas Latimer, May 16 2012
(PARI) A023811(n)=if(n>1, (n^n-n^2)\(n-1)^2+1) \\ M. F. Hasler, Jan 22 2013
(Magma) [0] cat [(n^n-n^2+n-1)/(n-1)^2: n in [2..20]]; // Vincenzo Librandi, May 22 2012
(Haskell)
a023811 n = foldl (\val dig -> val * n + dig) 0 [0 .. n - 1]
-- Reinhard Zumkeller, Aug 29 2014
(Python)
def a(n): return (n**n - n**2 + n - 1)//((n - 1)**2) if n > 1 else 0
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 24 2023
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
EXTENSIONS
Edited by M. F. Hasler, Jan 22 2013
STATUS
approved