A057226 Number of different symbols needed to express n as a Roman numeral.

1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 3, 3, 3, 2, 1, 2, 2, 2, 3, 2, 3, 3, 3, 2, 1, 2, 2, 2, 3, 2, 3, 3, 3, 2, 2, 3, 3, 3, 4, 3, 4, 4, 4, 3, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 3, 1, 2, 2, 2, 3, 2

Offset

1,4

Comments

Sequence created using classic Roman numerals, i.e., 99 = XCIX, not the questionable IC.

a(n) = a043537(A061493(n)). - Reinhard Zumkeller, Apr 14 2013

Links

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

Eric Weisstein's World of Mathematics, Roman Numerals

Wikipedia, Roman numerals

Example

a(97) = 4 as you need I, V, X and C to express XCVII.

Maple

with(StringTools): A057226 := proc(n) local r: r:=convert(n, roman): return `if`(Search("I", r)>0, 1, 0) + `if`(Search("V", r)>0, 1, 0) + `if`(Search("X", r)>0, 1, 0) + `if`(Search("L", r)>0, 1, 0) + `if`(Search("C", r)>0, 1, 0) + `if`(Search("D", r)>0, 1, 0) + `if`(Search("M", r)>0, 1, 0): end: seq(A057226(n), n=1..105); # Nathaniel Johnston, May 18 2011

Mathematica

Table[Length[Union[Characters[IntegerString[n, "Roman"]]]], {n, 110}] (* Harvey P. Dale, Mar 18 2013 *)

Prog

(Haskell)
a057226 = a043537 . a061493  -- Reinhard Zumkeller, Apr 14 2013

Crossrefs

Sequence in context: A230643 A344117 A163367 * A338260 A224963 A073810

Adjacent sequences: A057223 A057224 A057225 * A057227 A057228 A057229

Keyword

base,easy,nonn

Author

Helge T. Blohmer (crusher(AT)k-town.de), Sep 19 2000

Status

approved