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 A023811 Largest metadrome (number with digits in strict ascending order) in base n. 16
 0, 1, 5, 27, 194, 1865, 22875, 342391, 6053444, 123456789, 2853116705, 73686780563, 2103299351334, 65751519677857, 2234152501943159, 81985529216486895, 3231407272993502984, 136146740744970718253, 6106233505124424657789, 290464265927977839335179 (list; graph; refs; listen; history; text; internal format)
 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. 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 (MAGMA) [0] cat [(n^n-n^2+n-1)/(n-1)^2: n in [2..20]]; // Vincenzo Librandi, May 22 2012 (PARI) A023811(n)=if(n>1, (n^n-n^2)\(n-1)^2+1)  \\ M. F. Hasler, Jan 22 2013 (Haskell) a023811 n = foldl (\val dig -> val * n + dig) 0 [0 .. n - 1] -- Reinhard Zumkeller, Aug 29 2014 CROSSREFS Cf. A049363, A051846, A058128, A060073. Cf. A062813, A134640. Sequence in context: A326094 A232683 A240637 * A126119 A105631 A167019 Adjacent sequences:  A023808 A023809 A023810 * A023812 A023813 A023814 KEYWORD nonn,easy,base AUTHOR EXTENSIONS Edited by M. F. Hasler, Jan 22 2013 STATUS approved

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Last modified September 21 02:41 EDT 2020. Contains 337266 sequences. (Running on oeis4.)