A054986 Base-10 modest numbers.

13, 19, 23, 26, 29, 39, 46, 49, 59, 69, 79, 89, 103, 109, 111, 133, 199, 203, 206, 209, 211, 218, 222, 233, 266, 299, 309, 311, 327, 333, 399, 406, 409, 411, 412, 418, 422, 433, 436, 444, 466, 499, 509, 511, 515, 533, 545, 555, 599, 609, 611, 618, 622, 627

Offset

1,1

Comments

A number is modest if there exists at least one partitioning of its decimal expansion wherein the number divided by the second part leaves a remainder of the first part.

References

Problem 1291, J. Rec. Math., 17 (No.2, 1984), 140-141.

Links

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

Example

2036 is modest because 2036 mod 36 = 20. 2037 is modest because 2037 mod 037 = 2.

Prog

(Haskell)
import Data.List (inits, tails)
a054986 n = a054986_list !! (n-1)
a054986_list = filter modest [1..] where
   modest x = or $ zipWith m
              (map read $ (init $ tail $ inits $ show x) :: [Integer])
              (map read $ (tail $ init $ tails $ show x) :: [Integer])
      where m u v = u < v && (x - u) `mod` v == 0
-- Reinhard Zumkeller, Mar 26 2012
(PARI) is(n, p=1)=while(n>p*=10, n%p&&(n%(n%p)==n\p)&&return(1)) \\ M. F. Hasler, Sep 17 2014
(Python)
def ok(n):
    s = str(n)
    for i in range(1, len(s)):
        head, tail = int(s[:i]), int(s[i:])
        if tail and n%tail == head: return True
    return False
print([k for k in range(628) if ok(k)]) # Michael S. Branicky, Mar 28 2022

Crossrefs

Cf. A007627.

Sequence in context: A188540 A088184 A274407 * A210582 A071621 A240565

Adjacent sequences: A054983 A054984 A054985 * A054987 A054988 A054989

Keyword

easy,nonn,base

Author

Hans Havermann, May 30 2000

Status

approved