A237344 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(7).
0, 1, 2, 3, 4, 5, 6, 7, 49, 50, 51, 52, 53, 54, 55, 56, 57, 549, 550, 551, 552, 553, 554, 555, 556, 557, 5549, 5550, 5551, 5552, 5553, 5554, 5555, 5556, 5557, 55549, 55550, 55551, 55552, 55553, 55554, 55555, 55556, 55557, 555549, 555550, 555551, 555552
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).
Programs
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Mathematica
CoefficientList[Series[(10 x^17 - 20 x^16 - 10 x^15 + 10 x^13 + 20 x^12 + 30 x^11 + 40 x^10 + 50 x^9 + 49 x^8 + 7 x^7 + 6 x^6 + 5 x^5 + 4 x^4 + 3 x^3 + 2 x^2 + x)/(10 x^18 -11 x^9 + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 24 2014 *)
Formula
G.f.: (10*x^17 -20*x^16 -10*x^15 +10*x^13 +20*x^12 +30*x^11 +40*x^10 +50*x^9 +49*x^8 +7*x^7 +6*x^6 +5*x^5 +4*x^4 +3*x^3 +2*x^2 +x)/(10*x^18 -11*x^9 +1). - Alois P. Heinz, Feb 07 2014
Extensions
Definition by N. J. A. Sloane, Feb 07 2014