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 A030133 a(n+1) is the sum of digits of (a(n) + a(n-1)). 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)