A093785 Numbers that are divisible by every digit in their Roman numeral representation.

1, 2, 3, 5, 10, 20, 30, 50, 100, 200, 300, 500, 1000, 2000, 3000

Offset: 1

Author

Reinhard Zumkeller, May 17 2004

Keywords

• nonn
• base
• fini
• full

Comments

The sequence contains only values less than 4000, see A078715 for a discussion on the Roman 4M-problem.

Examples

			I, II, III, V, X, XX, XXX, L, C, CC, CCC, D, M, MM, MMM.
		

Links

• Stephanus Gibbs, Roman Numeral and Date Conversion
• Gerard Schildberger, The first 3999 numbers in Roman numerals
• Eric Weisstein's World of Mathematics, Roman Numerals
• Wikipedia, Roman numerals

Crossrefs

Cf. A034838.

Cf. A061493.

Programs

Haskell

a093785 n = a093785_list !! (n-1)
a093785_list = filter p [1..3999] where
   p v = q $ a061493 v where
     q w = w == 0 || v `mod` ([0,1,5,10,50,100,500,1000] !! d') == 0 && q w'
          where  (w',d) = divMod w 10; d' = fromInteger d
-- Reinhard Zumkeller, Apr 14 2013