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

0,3

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).

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

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 *)

Crossrefs

Cf. A235498, A235499, A237341 - A237346.

Sequence in context: A327733 A084831 A037406 * A024647 A250263 A024648

Adjacent sequences: A237341 A237342 A237343 * A237345 A237346 A237347

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Feb 06 2014

Extensions

Definition by N. J. A. Sloane, Feb 07 2014

Status

approved