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A030133 a(n+1) = sum of digits of (a(n) + a(n-1)). 6

%I

%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) = 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

%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

%Y Cf. A030132, A007953, A049341.

%K nonn,base,nice,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)