A093783 Sum of digits of n in Roman numeral representation.

1, 2, 3, 6, 5, 6, 7, 8, 11, 10, 11, 12, 13, 16, 15, 16, 17, 18, 21, 20, 21, 22, 23, 26, 25, 26, 27, 28, 31, 30, 31, 32, 33, 36, 35, 36, 37, 38, 41, 60, 61, 62, 63, 66, 65, 66, 67, 68, 71, 50, 51, 52, 53, 56, 55, 56, 57, 58, 61, 60, 61, 62, 63, 66, 65, 66, 67, 68

Offset

1,2

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..3999

Stephanus Gibbs, Roman Numeral and Date Conversion

Eric Weisstein's World of Mathematics, Roman Numerals

Wikipedia, Roman numerals

Example

n=42 == XLII: a(42) = 'X' + 'L' + 'I' + 'I' = 10+50+1+1 = 62.

Maple

A093783 := proc(n) local r: r:=convert(n, roman): return add(convert(r[j], arabic), j=1..length(r)): end: seq(A093783(n), n=1..68); # Nathaniel Johnston, May 18 2011

Mathematica

Total[#2 FromRomanNumeral[#1] & @@@ Tally[Characters@ RomanNumeral@ #]] & /@ Range@ 68 (* Michael De Vlieger, Sep 08 2015, Version 10.2 *)

Prog

(Haskell)
a093783 n = q 0 $ a061493 n where
     q s 0 = s
     q s x = q (s + [0, 1, 5, 10, 50, 100, 500, 1000] !! d') x'
             where  (x', d) = divMod x 10; d' = fromInteger d
-- Reinhard Zumkeller, Apr 14 2013

Crossrefs

Cf. A007953, A057226, A006968.

Cf. A061493, A002963.

Sequence in context: A337355 A384556 A392448 * A096861 A118738 A390954

Adjacent sequences: A093780 A093781 A093782 * A093784 A093785 A093786

Keyword

nonn,easy,base,changed

Author

Reinhard Zumkeller, May 17 2004

Status

approved