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A049363 a(1) = 1; for n>1, smallest digitally balanced number in base n. 12
1, 2, 11, 75, 694, 8345, 123717, 2177399, 44317196, 1023456789, 26432593615, 754777787027, 23609224079778, 802772380556705, 29480883458974409, 1162849439785405935, 49030176097150555672, 2200618769387072998445 (list; graph; refs; listen; history; text; internal format)
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

FORMULA

a(n)=(102345....n-1) in base n

Formula and more terms from 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

EXAMPLE

a(6) = (102345) in base 6 = 6^5+2*6^3+3*6^2+4*6+5 = 8345

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

CROSSREFS

Cf. A031443, A049354, A049355, A023811.

Sequence in context: A198088 A112894 A220878 * A055085 A209101 A118802

Adjacent sequences:  A049360 A049361 A049362 * A049364 A049365 A049366

KEYWORD

nonn,base,nice

AUTHOR

Harvey P. Dale

STATUS

approved

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Last modified December 22 19:34 EST 2014. Contains 252365 sequences.