A034709 - OEIS

A034709

Numbers divisible by their last digit.

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

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OFFSET

1,2

COMMENTS

Union of A017281, A017293, A139222, A139245, A017329, A139249, A139264, A139279 and A139280. - Reinhard Zumkeller, Jun 22 2008

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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..]

-- Reinhard Zumkeller, Jun 19 2011

(Python)

A034709_list = [n for n in range(1, 1000) if n % 10 and not n % (n % 10)]

# Chai Wah Wu, Sep 18 2014

(PARI) for(n=1, 200, if(n%10, if(!(n%digits(n)[#Str(n)]), print1(n, ", ")))) \\ Derek Orr, Sep 19 2014