A100830 Smallest number with same digital root as n but distinct from n and all earlier occurrences.

10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63

Offset

1,1

Comments

A010888(a(n)) = A010888(n) and a(n)<>n;

a(a(n))=n: self-inverse permutation of the natural numbers.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,-1,2,-1).

Formula

a(n) = n + 9*(-1)^floor((n-1)/9).

From Colin Barker, Sep 24 2019: (Start)

G.f.: x*(10 - 9*x - 8*x^9 + 9*x^10) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 - x^3 + x^6)).

a(n) = 2*a(n-1) - a(n-2) - a(n-9) + 2*a(n-10) - a(n-11) for n>11.

(End)

Mathematica

LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, -1, 2, -1}, {10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2}, 72] (* Metin Sariyar, Sep 24 2019 *)
Rest[CoefficientList[Series[x (10-9x-8x^9+9x^10)/((1-x)^2(1+x)(1-x+x^2)(1-x^3+x^6)), {x, 0, 80}], x]] (* Harvey P. Dale, Jul 20 2021 *)

Prog

(Haskell)
a100830 n  = n + 9 * (-1) ^ ((n - 1) `div` 9)
-- Reinhard Zumkeller, Aug 01 2014
(PARI) Vec(x*(10 - 9*x - 8*x^9 + 9*x^10) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 - x^3 + x^6)) + O(x^80)) \\ Colin Barker, Sep 24 2019

Crossrefs

Sequence in context: A342367 A303879 A305947 * A180176 A350494 A168100

Adjacent sequences: A100827 A100828 A100829 * A100831 A100832 A100833

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Jan 07 2005

Status

approved