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

Author

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

Keywords

• base
• easy
• nonn

Comments

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

Examples

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

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..3999
• Eric Weisstein's World of Mathematics, Roman Numerals
• Wikipedia, Roman numerals

Crossrefs

Cf. A043537, A061493.

Programs

Haskell

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

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 *)

Formula

a(n) = A043537(A061493(n)). - Reinhard Zumkeller, Apr 14 2013