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 A168183 Numbers that are not multiples of 9. 5
 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A168182(a(n)) = 1; complement of A008591; A010888(a(n)) = A010887(n-1); A109012(a(n)) < 9. It seems that, for any n >= 1, there exists no positive integer z such that digit_sum(z) = digit_sum(a(n)+z). - Max Lacoma, Sep 19 2019. Giovanni Resta: this follows immediately from the well-known fact that sod(x) == x (mod 9). LINKS Ivan Panchenko, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1). FORMULA From Wesley Ivan Hurt, Sep 12 2015: (Start) a(n) = a(n-1) + a(n-8) - a(n-9), n>9. a(n) = n + floor((n-1)/8). (End) From Philippe Deléham, Dec 05 2016: (Start) a(n) = 1 + A248375(n-1). G.f.: x*(1-x^9)/((1-x)^2*(1-x^8)). (End) E.g.f.: 1 + (1/8)*(-cos(x) + (-5+9*x)*cosh(x) - 2*cos(x/sqrt(2))*cosh(x/sqrt(2)) + sin(x) + (-4+9*x)*sinh(x) + 2*sin(x/sqrt(2))*(sqrt(2)*cosh(x/sqrt(2)) + sinh(x/sqrt(2)))). - Stefano Spezia, Sep 20 2019 MAPLE A168183:=n->n+floor((n-1)/8): seq(A168183(n), n=1..100); # Wesley Ivan Hurt, Sep 12 2015 MATHEMATICA Select[Table[n, {n, 200}], Mod[#, 9]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *) With[{nn=81}, Complement[Range[nn], 9Range[Floor[nn/9]]]] (* Harvey P. Dale, Sep 07 2011 *) PROG (Haskell) a168183 n = a168183_list !! (n-1) a168183_list = [1..8] ++ map (+ 9) a168183_list -- Reinhard Zumkeller, Mar 04 2014 (PARI) is(n)=!!(n%9) \\ Charles R Greathouse IV, Sep 02 2015 (PARI) a(n)=(9*n-1)\8 \\ Charles R Greathouse IV, Sep 02 2015 (MAGMA) [n+Floor((n-1)/8) : n in [1..100]]; // Wesley Ivan Hurt, Sep 12 2015 (Python) from gmpy2 import f_mod [n for n in range(100) if f_mod(n, 9)] # Bruno Berselli, Dec 05 2016 CROSSREFS Cf. A008591, A010887, A010888, A109012, A168182. Sequence in context: A194151 A020663 A255808 * A043094 A023803 A122132 Adjacent sequences:  A168180 A168181 A168182 * A168184 A168185 A168186 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, Nov 30 2009 STATUS approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)