A076314 a(n) = floor(n/10) + (n mod 10).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14

Offset: 0

Author

Reinhard Zumkeller, Oct 06 2002

Keywords

• nonn
• easy

Comments

For n<100 this is equal to the digital sum of n (see A007953). - Hieronymus Fischer, Jun 17 2007

Examples

			a(15) = floor(15 / 10) + (15 mod 10) = 1 + 5 = 6. - _Indranil Ghosh_, Feb 13 2017
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A076313, A010879, A076309, A076310, A076311, A076312, A055017, A007953, A003132.

Programs

Haskell

a076314 = uncurry (+) . flip divMod 10 -- Reinhard Zumkeller, Jun 01 2013

Magma

[n-9*Floor(n/10):n in [0..100]]; // Vincenzo Librandi, Dec 10 2016

Mathematica

Table[n - 9 Floor[n / 10], {n, 0, 100}] (* Vincenzo Librandi Dec 10 2016 *)

PARI

a(n)=n\10+n%10 \\ Charles R Greathouse IV, Sep 24 2015

Python

def A076314(n): return (n/10)+(n%10) # Indranil Ghosh, Feb 13 2017

Formula

From Hieronymus Fischer, Jun 17 2007: (Start)

a(n) = n - 9*floor(n/10).

a(n) = (n + 9*(n mod 10))/10.

a(n) = n - 9*A002266(A004526(n)) = n - 9*A004526(A002266(n)).

a(n) = (n + 9*A010879(n))/10.

a(n) = (n + 9*A000035(n) + 18*A010874(A004526(n)))/10.

a(n) = (n + 9*A010874(n) + 45*A000035(A002266(n)))/10.

G.f.: x*(8*x^10 - 9*x^9 + 1)/((1 - x^10)*(1 - x)^2). (End)

a(n) = A033930(n) for 1 <= n < 100. - R. J. Mathar, Sep 21 2008

a(n) = +a(n-1) + a(n-10) - a(n-11). - R. J. Mathar, Feb 20 2011