A030133 a(n+1) is the sum of digits of (a(n) + a(n-1)).

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, 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, 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

Offset

0,1

Comments

a(n) = A010888(A000032(n)). - Reinhard Zumkeller, Aug 20 2011

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.

Decimal expansion of 23719213606865169775282 / 111111111111111111111111 = 0.[213472922461786527977538] (periodic). - Daniel Forgues, Feb 27 2017

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, 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).

Formula

a(n+24) = a(n); a(A017593(n)) = 9. - Reinhard Zumkeller, Jul 04 2007

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

Mathematica

Transpose[NestList[{Last[#], Total[IntegerDigits[Total[#]]]}&, {2, 1}, 100]] [[1]] (* Harvey P. Dale, Jul 25 2011 *)

Prog

(Haskell)
a030133 n = a030133_list !! n
a030133_list =
   2 : 1 : map a007953 (zipWith (+) a030133_list $ tail a030133_list)
-- Reinhard Zumkeller, Aug 20 2011
(PARI) V=[2, 1]; for(n=1, 100, V=concat(V, sumdigits(V[n]+V[n+1]))); V \\ Derek Orr, Feb 27 2017
(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

Crossrefs

Cf. A030132, A007953, A049341.

Sequence in context: A358642 A060214 A259773 * A139374 A111958 A192439

Adjacent sequences: A030130 A030131 A030132 * A030134 A030135 A030136

Keyword

nonn,base,nice,easy

Author

N. J. A. Sloane

Status

approved