|
|
A034709
|
|
Numbers divisible by their last digit.
|
|
35
|
|
|
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, 51, 52, 55, 61, 62, 63, 64, 65, 66, 71, 72, 75, 77, 81, 82, 84, 85, 88, 91, 92, 93, 95, 96, 99, 101, 102, 104, 105, 111, 112, 115, 121, 122, 123, 124, 125, 126, 128, 131, 132
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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
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
|
|
LINKS
|
|
|
MAPLE
|
N:= 1000: # to get all terms <= N
sort([seq(seq(ilcm(10, d)*x+d, x=0..floor((N-d)/ilcm(10, d))), d=1..9)]); # Robert Israel, Aug 20 2015
|
|
MATHEMATICA
|
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 *)
Select[Range[150], Mod[#, 10]!=0&&Divisible[#, Mod[#, 10]]&] (* Harvey P. Dale, Aug 07 2022 *)
|
|
PROG
|
(Haskell)
import Data.Char (digitToInt)
a034709 n = a034709_list !! (n-1)
a034709_list =
filter (\i -> i `mod` 10 > 0 && i `mod` (i `mod` 10) == 0) [1..]
(Python)
A034709_list = [n for n in range(1, 1000) if n % 10 and not n % (n % 10)]
(PARI) for(n=1, 200, if(n%10, if(!(n%digits(n)[#Str(n)]), print1(n, ", ")))) \\ Derek Orr, Sep 19 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|