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
KEYWORD
easy,nonn,base
AUTHOR
Hans Havermann, May 30 2000
STATUS
approved