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A049363
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a(1) = 1; for n>1, smallest digitally balanced number in base n.
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21
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1, 2, 11, 75, 694, 8345, 123717, 2177399, 44317196, 1023456789, 26432593615, 754777787027, 23609224079778, 802772380556705, 29480883458974409, 1162849439785405935, 49030176097150555672, 2200618769387072998445, 104753196945250864004691, 5271200265927977839335179
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..250
Eric Weisstein's World of Mathematics, Pandigital Number
Wikipedia, Pandigital number
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FORMULA
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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
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EXAMPLE
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a(6) = (102345) in base 6 = 6^5 + 2*6^3 + 3*6^2 + 4*6 + 5 = 8345.
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MAPLE
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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
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MATHEMATICA
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Table[FromDigits[Join[{1, 0}, Range[2, n-1]], n], {n, 20}] (* Harvey P. Dale, Oct 12 2012 *)
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PROG
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(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
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CROSSREFS
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Column k=1 of A061845 (for n>1).
Cf. A031443, A049354, A049355, A023811.
Sequence in context: A198088 A112894 A220878 * A055085 A209101 A118802
Adjacent sequences: A049360 A049361 A049362 * A049364 A049365 A049366
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KEYWORD
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nonn,base,nice
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AUTHOR
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Harvey P. Dale
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EXTENSIONS
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More terms from Ulrich Schimke (ulrschimke(AT)aol.com)
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STATUS
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approved
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