A049363 a(1) = 1; for n > 1, smallest digitally balanced number in base n.

1, 2, 11, 75, 694, 8345, 123717, 2177399, 44317196, 1023456789, 26432593615, 754777787027, 23609224079778, 802772380556705, 29480883458974409, 1162849439785405935, 49030176097150555672, 2200618769387072998445, 104753196945250864004691, 5271200265927977839335179

Offset

1,2

Comments

A037968(a(n)) = n and A037968(m) < n for m < a(n). - Reinhard Zumkeller, Oct 27 2003

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

Column k=1 of A061845 (for n>1).

Cf. A031443, A049354, A049355, A023811.

Sequence in context: A198088 A112894 A220878 * A055085 A354298 A350580

Adjacent sequences: A049360 A049361 A049362 * A049364 A049365 A049366

Keyword

nonn,base,nice

Author

Harvey P. Dale

Extensions

More terms from Ulrich Schimke (ulrschimke(AT)aol.com)

Status

approved