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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice
• easy

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).

Crossrefs

Cf. A030132, A007953, A049341.

Programs

Haskell

a030133 n = a030133_list !! n
a030133_list =
   2 : 1 : map a007953 (zipWith (+) a030133_list $ tail a030133_list)
-- Reinhard Zumkeller, Aug 20 2011

Mathematica

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

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