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

Author

Reinhard Zumkeller, May 17 2004

Keywords

• nonn
• easy
• base

Examples

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

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

Crossrefs

Cf. A007953, A057226, A006968.

Cf. A061493, A002963.

Programs

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
(HP 49G calculator)
::
  CK1&Dispatch
  # FF
  ::
    FPTR2 ^DupQIsZero?
    caseSIZEERR
    FPTR2 ^Z>S
    Z0_
    SWAP
    DUPLEN$
    ZERO_DO
    DUP
    ISTOP-INDEX
    SUB$1#
    BINT48
    #-
    BINT4
    OVER#=
    OVER
    BINT9
    #=
    OR
    IT
    #2+
    FPTR2 ^#>Z
    Z10_
    INDEX@
    FPTR2 ^RP#
    FPTR2 ^RMULText
    ROT
    FPTR2 ^RADDext
    SWAPLOOP
    DROP
  ;
;
Gerald Hillier, Sep 08 2015

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 *)