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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). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

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

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 *)

PROG

(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

CROSSREFS

Cf. A235498, A235499, A237341 - A237346.

Sequence in context: A298525 A081101 A043059 * A247635 A152754 A001560

Adjacent sequences:  A237412 A237413 A237414 * A237416 A237417 A237418

KEYWORD

nonn,base,easy

AUTHOR

Vincenzo Librandi, Feb 07 2014

EXTENSIONS

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

STATUS

approved

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)