%I #28 Sep 08 2022 08:45:07

%S 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,

%T 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,

%U 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

%N a(n) = floor(n/10) + (n mod 10).

%C For n<100 this is equal to the digital sum of n (see A007953). - _Hieronymus Fischer_, Jun 17 2007

%H Reinhard Zumkeller, <a href="/A076314/b076314.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).

%F From _Hieronymus Fischer_, Jun 17 2007: (Start)

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

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

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

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

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

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

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

%F a(n) = A033930(n) for 1 <= n < 100. - _R. J. Mathar_, Sep 21 2008

%F a(n) = +a(n-1) + a(n-10) - a(n-11). - _R. J. Mathar_, Feb 20 2011

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

%t Table[n - 9 Floor[n / 10], {n, 0, 100}] (* _Vincenzo Librandi_ Dec 10 2016 *)

%o (Haskell)

%o a076314 = uncurry (+) . flip divMod 10 -- _Reinhard Zumkeller_, Jun 01 2013

%o (PARI) a(n)=n\10+n%10 \\ _Charles R Greathouse IV_, Sep 24 2015

%o (Magma) [n-9*Floor(n/10):n in [0..100]]; // _Vincenzo Librandi_, Dec 10 2016

%o (Python) def A076314(n): return (n/10)+(n%10) # _Indranil Ghosh_, Feb 13 2017

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

%K nonn,easy

%O 0,3

%A _Reinhard Zumkeller_, Oct 06 2002