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

1,2

Comments

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

Links

Table of n, a(n) for n=1..15.

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

Example

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

Prog

(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

Crossrefs

Cf. A034838.

Cf. A061493.

Sequence in context: A054317 A065840 A181934 * A105369 A047101 A251703

Adjacent sequences: A093782 A093783 A093784 * A093786 A093787 A093788

Keyword

nonn,base,fini,full

Author

Reinhard Zumkeller, May 17 2004

Status

approved