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%I #35 Sep 25 2019 07:48:08
%S 2,1,3,4,7,2,9,2,2,4,6,1,7,8,6,5,2,7,9,7,7,5,3,8,2,1,3,4,7,2,9,2,2,4,
%T 6,1,7,8,6,5,2,7,9,7,7,5,3,8,2,1,3,4,7,2,9,2,2,4,6,1,7,8,6,5,2,7,9,7,
%U 7,5,3,8,2,1,3,4,7,2,9,2,2,4,6,1,7,8,6,5,2,7,9,7,7,5,3,8,2,1,3
%N a(n+1) is the sum of digits of (a(n) + a(n-1)).
%C a(n) = A010888(A000032(n)). - _Reinhard Zumkeller_, Aug 20 2011
%C Similar to the digital roots of several Fibonacci sequences, this digital root sequence for Lucas numbers (A000032) has period 24 with digits summing to 117.
%C Decimal expansion of 23719213606865169775282 / 111111111111111111111111 = 0.[213472922461786527977538] (periodic). - _Daniel Forgues_, Feb 27 2017
%H Reinhard Zumkeller, <a href="/A030133/b030133.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F a(n+24) = a(n); a(A017593(n)) = 9. - _Reinhard Zumkeller_, Jul 04 2007
%F G.f.: (2 + x + 3*x^2 + 4*x^3 + 7*x^4 + 2*x^5 + 9*x^6 + 2*x^7 + 2*x^8 + 4*x^9 + 6*x^10 + x^11 + 7*x^12 + 8*x^13 + 6*x^14 + 5*x^15 + 2*x^16 + 7*x^17 + 9*x^18 + 7*x^19 + 7*x^20 + 5*x^21 + 3*x^22 + 8*x^23) / (1 - x^24). - _Colin Barker_, Sep 25 2019
%t Transpose[NestList[{Last[#],Total[IntegerDigits[Total[#]]]}&, {2,1}, 100]] [[1]] (* _Harvey P. Dale_, Jul 25 2011 *)
%o (Haskell)
%o a030133 n = a030133_list !! n
%o a030133_list =
%o 2 : 1 : map a007953 (zipWith (+) a030133_list $ tail a030133_list)
%o -- _Reinhard Zumkeller_, Aug 20 2011
%o (PARI) V=[2,1];for(n=1,100,V=concat(V,sumdigits(V[n]+V[n+1])));V \\ _Derek Orr_, Feb 27 2017
%o (PARI) Vec((2 + x + 3*x^2 + 4*x^3 + 7*x^4 + 2*x^5 + 9*x^6 + 2*x^7 + 2*x^8 + 4*x^9 + 6*x^10 + x^11 + 7*x^12 + 8*x^13 + 6*x^14 + 5*x^15 + 2*x^16 + 7*x^17 + 9*x^18 + 7*x^19 + 7*x^20 + 5*x^21 + 3*x^22 + 8*x^23) / (1 - x^24) + O(x^80)) \\ _Colin Barker_, Sep 25 2019
%Y Cf. A030132, A007953, A049341.
%K nonn,base,nice,easy
%O 0,1
%A _N. J. A. Sloane_
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