A081596 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 5x+y.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 35, 36, 37, 38, 39, 40, 41

Offset: 0

Author

N. J. A. Sloane, Apr 22 2003

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A081502. Different from A028900.

Programs

Magma

k:=5; [n-(10-k)*Floor(n/10): n in [0..100]]; // Bruno Berselli, Jun 24 2014

Mathematica

CoefficientList[Series[-x (4 x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1)/((x - 1)^2 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 150}], x] (* Vincenzo Librandi, Jun 25 2014 *)

PARI

my(n, x, y); vector(200, n, y=(n-1)%10; x=(n-1-y)\10; 5*x+y) \\ Colin Barker, Jun 24 2014

Formula

G.f.: -x*(4*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -x^3 -x^2 -x -1) / ((x -1)^2*(x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Jun 24 2014

a(n) = n - 5*floor(n/10). [Bruno Berselli, Jun 24 2014]