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%I #18 Jul 20 2021 17:53:52
%S 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,
%T 36,19,20,21,22,23,24,25,26,27,46,47,48,49,50,51,52,53,54,37,38,39,40,
%U 41,42,43,44,45,64,65,66,67,68,69,70,71,72,55,56,57,58,59,60,61,62,63
%N Smallest number with same digital root as n but distinct from n and all earlier occurrences.
%C A010888(a(n)) = A010888(n) and a(n)<>n;
%C a(a(n))=n: self-inverse permutation of the natural numbers.
%H Reinhard Zumkeller, <a href="/A100830/b100830.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,-1,2,-1).
%F a(n) = n + 9*(-1)^floor((n-1)/9).
%F From _Colin Barker_, Sep 24 2019: (Start)
%F 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)).
%F a(n) = 2*a(n-1) - a(n-2) - a(n-9) + 2*a(n-10) - a(n-11) for n>11.
%F (End)
%t 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 *)
%t 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 *)
%o (Haskell)
%o a100830 n = n + 9 * (-1) ^ ((n - 1) `div` 9)
%o -- _Reinhard Zumkeller_, Aug 01 2014
%o (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
%K nonn,base,easy
%O 1,1
%A _Reinhard Zumkeller_, Jan 07 2005
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