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

Author

Hans Havermann, May 30 2000

Keywords

• easy
• nonn
• base

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.

Examples

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

References

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

Links

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

Crossrefs

Cf. A007627.

Programs

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