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 A051885 Smallest number whose sum of digits is n. 41
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 199999, 299999, 399999, 499999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is also the list of lunar triangular numbers: A087052 with duplicates removed. - N. J. A. Sloane, Jan 25 2011 Numbers n such that A061486(n) = n. - Amarnath Murthy, May 06 2001 The product of digits incremented by 1 is the same as the number incremented by 1. If a(n) = abcd...(a,b,c,d, etc. are digits of a(n)) {a(n) + 1} = (a+1)*(b+1)(c+1)*(d+1)*..., e.g., 299 + 1 = (2+1)*(9+1)*(9+1) = 300. - Amarnath Murthy, Jul 29 2003 A138471(a(n)) = 0. - Reinhard Zumkeller, Mar 19 2008 a(n+1) = A108971(A179988(n)). - Reinhard Zumkeller, Aug 09 2010, Jul 10 2011 Positions of records in A003132: A080151(n) = A003132(a(n)). - Reinhard Zumkeller, Jul 10 2011 a(n) = A242614(n,1). - Reinhard Zumkeller, Jul 16 2014 A254524(a(n)) = 1. - Reinhard Zumkeller, Oct 09 2015 The slowest strictly increasing sequence of nonnegative integers such that, for any two terms, calculating the difference of their decimal representations requires no borrowing. - Rick L. Shepherd, Aug 11 2017 LINKS Iain Fox, Table of n, a(n) for n = 0..9000 (first 101 terms from Reinhard Zumkeller) D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing] A. Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000. Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10). FORMULA These are the numbers i*10^j-1 (i=1..9, j >= 0). - N. J. A. Sloane, Jan 25 2011 a(n) = ((n mod 9) + 1)*10^floor(n/9) - 1 = a(n-1) + 10^floor((n-1)/9). - Henry Bottomley, Apr 24 2001 a(n) = A037124(n+1) - 1. - Reinhard Zumkeller, Jan 03 2008, Jul 10 2011 G.f.: x*(x^2+x+1)*(x^6+x^3+1) / ((x-1)*(10*x^9-1)). - Colin Barker, Feb 01 2013 MAPLE P:=proc(n) local i, w, x; for i from 0 by 1 to n do w:=trunc(i/9); x:=(i-9*w)*10^w; while w>0 do x:=x+9*10^(w-1); w:=w-1; od; print(x); od; end: P(100); # Paolo P. Lava, Mar 11 2008 b:=10; t1:=[]; for j from 0 to 15 do for i from 1 to b-1 do t1:=[op(t1), i*b^j-1]; od: od: t1; # N. J. A. Sloane, Jan 25 2011 MATHEMATICA a[n_] := (Mod[n, 9] + 1)*10^Floor[n/9] - 1; Table[a[n], {n, 0, 49}](* Jean-François Alcover, Dec 01 2011, after Henry Bottomley *) PROG (Haskell) a051885 n = (m + 1) * 10^n' - 1 where (n', m) = divMod n 9 -- Reinhard Zumkeller, Jul 10 2011 (MAGMA) [i*10^j-1: i in [1..9], j in [0..5]]; (PARI) A051885(n) = (n%9+1)*10^(n\9)-1  \\ M. F. Hasler, Jun 17 2012 (PARI) first(n) = Vec(x*(x^2 + x + 1)*(x^6 + x^3 + 1)/((x - 1)*(10*x^9 - 1)) + O(x^n), -n) \\ Iain Fox, Dec 30 2017 CROSSREFS Cf. A061104, A061105, A061486, A007953, A067043, A087052. Numbers of form i*b^j-1 (i=1..b-1, j >= 0) for bases b = 2 through 9: A000225, A062318, A180516, A181287, A181288, A181303, A165804, A140576. - N. J. A. Sloane, Jan 25 2011 Cf. A002283. Cf. A254524. Sequence in context: A088473 A317110 A190876 * A227378 A226637 A274841 Adjacent sequences:  A051882 A051883 A051884 * A051886 A051887 A051888 KEYWORD nonn,easy,base,nice,look AUTHOR Felice Russo, Dec 15 1999 EXTENSIONS More terms from James A. Sellers, Dec 16 1999 Offset fixed by Reinhard Zumkeller, Jul 10 2011 STATUS approved

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Last modified August 26 03:38 EDT 2019. Contains 326324 sequences. (Running on oeis4.)