A235499 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(3).

0, 1, 2, 3, 9, 10, 11, 12, 13, 19, 20, 21, 22, 23, 29, 30, 31, 32, 33, 39, 40, 41, 42, 43, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 69, 70, 71, 72, 73, 79, 80, 81, 82, 83, 89, 90, 91, 92, 93, 99, 100, 101, 102, 103, 109, 110, 111, 112, 113, 119, 120, 121, 122, 123, 129

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

G.f.: (x^5+6*x^4+x^3+x^2+x)/(x^6-x^5-x+1). - Alois P. Heinz, Feb 07 2014

Mathematica

CoefficientList[Series[(x^5 + 6 x^4 + x^3 + x^2 + x)/(x^6 - x^5 - x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 08 2014 *)
nxt[n_]:=If[Mod[n, 10]==3, FromDigits[Join[Most[IntegerDigits[n]], {9}]], n+ 1]; NestList[nxt, 0, 70] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 9, 10}, 70] (* Harvey P. Dale, Oct 02 2016 *)

Crossrefs

Cf. A235498, A237341, A237342, A237343, A237344, A237345, A237346.

Sequence in context: A163905 A353653 A351650 * A242590 A135204 A037463

Adjacent sequences: A235496 A235497 A235498 * A235500 A235501 A235502

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Feb 06 2014

Extensions

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

Status

approved