A168183 Numbers that are not multiples of 9.

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

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 A353511

Adjacent sequences: A168180 A168181 A168182 * A168184 A168185 A168186

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 30 2009

Status

approved