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 A054986 Base-10 modest numbers. 4
 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)
 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

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Last modified August 10 03:28 EDT 2022. Contains 356029 sequences. (Running on oeis4.)