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A034709 Numbers divisible by their last digit.

%I A034709 #47 Nov 24 2022 04:21:23
%S A034709 1,2,3,4,5,6,7,8,9,11,12,15,21,22,24,25,31,32,33,35,36,41,42,44,45,48,
%T A034709 51,52,55,61,62,63,64,65,66,71,72,75,77,81,82,84,85,88,91,92,93,95,96,
%U A034709 99,101,102,104,105,111,112,115,121,122,123,124,125,126,128,131,132
%N A034709 Numbers divisible by their last digit.
%C A034709 Union of A017281, A017293, A139222, A139245, A017329, A139249, A139264, A139279 and A139280. - _Reinhard Zumkeller_, Jun 22 2008
%C A034709 The differences between consecutive terms repeat with period 1177 and the corresponding terms differ by 2520 = LCM(1,2,...,9). In other words, a(k*1177+i) = 2520*k + a(i). - _Giovanni Resta_, Aug 20 2015
%C A034709 The asymptotic density of this sequence is 1177/2520 = 0.467063... (see A341431 and A341432 for the values in other base representations). - _Amiram Eldar_, Nov 24 2022
%H A034709 Reinhard Zumkeller, <a href="/A034709/b034709.txt">Table of n, a(n) for n = 1..10000</a>
%p A034709 N:= 1000: # to get all terms <= N
%p A034709 sort([seq(seq(ilcm(10,d)*x+d, x=0..floor((N-d)/ilcm(10,d))), d=1..9)]); # _Robert Israel_, Aug 20 2015
%t A034709 dldQ[n_]:=Module[{idn=IntegerDigits[n],last1},last1=Last[idn]; last1!= 0&&Divisible[n,last1]]; Select[Range[150],dldQ]  (* _Harvey P. Dale_, Apr 25 2011 *)
%t A034709 Select[Range[150],Mod[#,10]!=0&&Divisible[#,Mod[#,10]]&] (* _Harvey P. Dale_, Aug 07 2022 *)
%o A034709 (Haskell)
%o A034709 import Data.Char (digitToInt)
%o A034709 a034709 n = a034709_list !! (n-1)
%o A034709 a034709_list =
%o A034709    filter (\i -> i `mod` 10 > 0 && i `mod` (i `mod` 10) == 0) [1..]
%o A034709 -- _Reinhard Zumkeller_, Jun 19 2011
%o A034709 (Python)
%o A034709 A034709_list = [n for n in range(1, 1000) if n % 10 and not n % (n % 10)]
%o A034709 # _Chai Wah Wu_, Sep 18 2014
%o A034709 (PARI) for(n=1,200,if(n%10,if(!(n%digits(n)[#Str(n)]),print1(n,", ")))) \\ _Derek Orr_, Sep 19 2014
%Y A034709 Cf. A010879, A034838, A007602.
%Y A034709 Cf. A017281, A017293, A139222, A139245, A017329, A139249, A139264, A139279, A139280.
%Y A034709 Cf. A341431, A341432.
%K A034709 nonn,base,easy,nice
%O A034709 1,2
%A A034709 _Erich Friedman_