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
(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

Crossrefs

Cf. A007953, A057226, A006968.

Cf. A061493, A002963.

Sequence in context: A327669 A253413 A337355 * A096861 A118738 A175067

Adjacent sequences: A093780 A093781 A093782 * A093784 A093785 A093786

Keyword

nonn,easy,base

Author

Reinhard Zumkeller, May 17 2004

Status

approved