A237415 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^3. This is k(2).

0, 1, 2, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 28, 29, 30, 31, 32, 38, 39, 40, 41, 42, 48, 49, 50, 51, 52, 58, 59, 60, 61, 62, 68, 69, 70, 71, 72, 78, 79, 80, 81, 82, 88, 89, 90, 91, 92, 98, 99, 100, 101, 102, 108, 109, 110, 111, 112, 118, 119, 120, 121, 122, 128

Offset: 0

Author

Vincenzo Librandi, Feb 07 2014

Keywords

• nonn
• base
• easy

Comments

Nonnegative integers m such that floor(2*m^2/10) = 2*floor(m^2/10). [Bruno Berselli, Dec 08 2015]

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).

Crossrefs

Cf. A235498, A235499, A237341 - A237346.

Programs

Magma

I:=[0,1,2,8,9,10]; [n le 6 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..80]]; // Vincenzo Librandi, Feb 12 2014

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 8, 9, 10}, 70] (* Bruno Berselli, Feb 08 2014 *)
CoefficientList[Series[x (1 + x + 6 x^2 + x^3 + x^4)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 12 2014 *)
NestList[If[Mod[#,10]==2,FromDigits[Join[Most[IntegerDigits[#]],{8}]], #+ 1]&,0,100] (* Harvey P. Dale, Feb 21 2016 *)

Formula

G.f.: x*(1 + x + 6*x^2 + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)). [Bruno Berselli, Feb 08 2014]

a(n) = a(n-1)+a(n-5)-a(n-6). - Vincenzo Librandi, Feb 12 2014

Extensions

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