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

Author

Vincenzo Librandi, Feb 06 2014

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. A235498, A235499, A237341 - A237346.

Programs

Mathematica

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

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]

Extensions

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