A028899 -id:A028899 - cp's OEIS frontend

A081595 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 4x+y.

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

Offset: 0

N. J. A. Sloane, Apr 22 2003

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).

Cf. A081502. Starts to differ from A028899 at a(100).

k:=4; [n-(10-k)*Floor(n/10): n in [0..100]]; // Bruno Berselli, Jun 24 2014

CoefficientList[Series[-x (5 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 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,8,9,4},80] (* Harvey P. Dale, Sep 17 2023 *)

my(n, x, y); vector(200, n, y=(n-1)%10; x=(n-1-y)\10; 4*x+y) \\ Colin Barker, Jun 24 2014

G.f.: -x*(5*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 - 6*floor(n/10). [Bruno Berselli, Jun 24 2014]

A083291 Triangular array read by rows: T(n,k) = k*floor(n/10) + n mod 10, 0<=k<=n.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 3, 4, 5, 6, 7, 8, 9, 10, 11

Offset: 0

Reinhard Zumkeller, Apr 23 2003

A010879(n)=T(n,0);
A076314(0)=T(0,0), A076314(n)=T(n,1) for n>0;
A028897(n)=T(n,n) for n<=1, A028897(n)=T(n,2) for n>1;
A028898(n)=T(n,n) for n<=2, A028898(n)=T(n,3) for n>2;
A028899(n)=T(n,n) for n<=3, A028899(n)=T(n,4) for n>3;
A028900(n)=T(n,n) for n<=4, A028900(n)=T(n,5) for n>4;
A028901(n)=T(n,n) for n<=5, A028901(n)=T(n,6) for n>5;
A028902(n)=T(n,n) for n<=6, A028902(n)=T(n,7) for n>6;
A028903(n)=T(n,n) for n<=7, A028903(n)=T(n,8) for n>7;
A028904(n)=T(n,n) for n<=8, A028904(n)=T(n,9) for n>8;
T(n,n) = n for n<=9, T(n,10) = n for n>9;
A083292(n) = T(n,n).

			From _Paolo Xausa_, May 22 2024: (Start)
Triangle begins:
   [0] 0;
   [1] 1, 1;
   [2] 2, 2, 2;
   [3] 3, 3, 3, 3;
   [4] 4, 4, 4, 4, 4;
   [5] 5, 5, 5, 5, 5, 5;
   [6] 6, 6, 6, 6, 6, 6, 6;
   [7] 7, 7, 7, 7, 7, 7, 7, 7;
   [8] 8, 8, 8, 8, 8, 8, 8, 8, 8;
   [9] 9, 9, 9, 9, 9, 9, 9, 9, 9, 9;
  [10] 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
  ... (End)

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).

Table[k*Floor[n/10] + Mod[n, 10], {n, 0, 10}, {k, 0, n}]//Flatten (* Paolo Xausa, May 22 2024 *)

Offset changed to 0 by Paolo Xausa, May 22 2024

cp's OEIS Frontend

A081595 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 4x+y.

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