A237342 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(5).

0, 1, 2, 3, 4, 5, 25, 225, 2225, 22225, 222225, 2222225, 22222225, 222222225, 2222222225, 22222222225, 222222222225, 2222222222225, 22222222222225, 222222222222225, 2222222222222225, 22222222222222225, 222222222222222225, 2222222222222222225

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (11, -10).

Formula

G.f.: (10*x^6-9*x^5-9*x^4-9*x^3-9*x^2+x)/(10*x^2-11*x+1). - Alois P. Heinz, Feb 07 2014

a(n) = ( 25 + 2*10^(n-4) )/9 for n>4. [Bruno Berselli, Feb 08 2014]

Mathematica

Join[Range[0, 4], Table[(25 + 2 10^(n - 4))/9, {n, 5, 30}]] (* Bruno Berselli, Feb 08 2014 *)

Crossrefs

Cf. A235498, A235499, A237341 - A237346.

Sequence in context: A242799 A281588 A088865 * A075807 A124232 A051143

Adjacent sequences: A237339 A237340 A237341 * A237343 A237344 A237345

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Feb 06 2014

Extensions

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

Status

approved