A034837 Numbers that are divisible by the first, i.e., the leftmost, digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• base
• nice
• look
• easy

Comments

A 10-automatic sequence. - Charles R Greathouse IV, Jun 13 2017

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A034709 (divisible by last digit).

Programs

Haskell

import Data.Char (digitToInt)
a034837 n = a034837_list !! (n-1)
a034837_list = filter (\i -> i `mod` (a000030 i) == 0) [1..]
-- Reinhard Zumkeller, Jun 19 2011

Mathematica

Select[Range[150],Divisible[#,IntegerDigits[#][[1]]]&] (* Harvey P. Dale, Jul 11 2017 *)

PARI

for(n=1,1000,n%(Vecsmall(Str(n))[1]-48) || print1(n",")) \\ M. F. Hasler, Jun 19 2011

PARI

a(n)=for(k=1,1e9,k%(Vecsmall(Str(k))[1]-48) || n-- || return(k)) \\  M. F. Hasler, Jun 19 2011

Python

def ok(n): return n and n%int(str(n)[0]) == 0
print([k for k in range(123) if ok(k)]) # Michael S. Branicky, Jan 15 2023

Python

from itertools import count, islice
def agen(): # generator of terms
    yield from (i for e in count(0) for f in range(1, 10) for i in range(f*10**e, (f+1)*10**e, f))
print(list(islice(agen(), 64))) # Michael S. Branicky, Jan 15 2023

Formula

a(n) mod A000030(a(n)) = 0. - Reinhard Zumkeller, Sep 20 2003

Extensions

Definition clarified by Harvey P. Dale, May 01 2023