A192333 Numbers that are "unsafe" when playing the game Dollar Nim, which is a Nim game where users can remove 1, 5, 10, or 25 cents from an initial pile of money. The most common version of the game is played with an initial amount of $1, hence the name.

0, 2, 4, 6, 8, 15, 17, 19, 21, 23, 30, 32, 34, 36, 38, 45, 47, 49, 51, 53, 60, 62, 64, 66, 68, 75, 77, 79, 81, 83, 90, 92, 94, 96, 98, 105, 107, 109, 111, 113, 120, 122, 124, 126, 128, 135, 137, 139, 141, 143, 150, 152, 154, 156, 158, 165

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

a(n) = 5*floor((n-1)/5) + 2*n - 2.

G.f.: x^2*(2 + 2*x + 2*x^2 + 2*x^3 + 7*x^4)/((x^4 + x^3 + x^2 + x + 1)*(x-1)^2). - R. J. Mathar, Jun 28 2011

Example

For n = 2, a pile with 2 cents remaining is unsafe because the player would only be able to remove a penny, leaving the opponent with 1 cent and a guaranteed win.

Prog

(Magma) [5*Floor((n-1)/5) + 2*n - 2: n in [1..60]]; // Vincenzo Librandi, Jul 04 2011

Crossrefs

Sequence in context: A317979 A359090 A167229 * A068902 A269332 A077569

Adjacent sequences: A192330 A192331 A192332 * A192334 A192335 A192336

Keyword

nonn,easy

Author

Patrick Vennebush, Jun 28 2011

Status

approved