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A054986
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Base-10 modest numbers.
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4
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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Problem 1291, J. Rec. Math., 17 (No.2, 1984), 140-141.
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LINKS
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EXAMPLE
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2036 is modest because 2036 mod 36 = 20. 2037 is modest because 2037 mod 037 = 2.
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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