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

1,2

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.

Formula

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A034709 (divisible by last digit).

Sequence in context: A247756 A375758 A032520 * A096105 A178157 A246083

Adjacent sequences: A034834 A034835 A034836 * A034838 A034839 A034840

Keyword

nonn,base,nice,look,easy

Author

Erich Friedman

Extensions

Definition clarified by Harvey P. Dale, May 01 2023

Status

approved