A120433 Numbers whose Roman numeral representation uses the subtractive notation.

4, 9, 14, 19, 24, 29, 34, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 59, 64, 69, 74, 79, 84, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 109, 114, 119, 124, 129, 134, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154, 159, 164, 169, 174

Offset: 1

Author

Christian Amet, Jul 13 2006

Keywords

• base
• nonn

Comments

Each number in this sequence has a 4 or a 9 in its decimal representation, corresponding to one of IV, IX, XL, XC, CD, CM. - Alonso del Arte, Jan 05 2018

Examples

			In Roman numerals, 14 is XIV, that is, X + (V - I) = 10 + (5 - 1) = 14, so 14 is in the sequence.
In Roman numerals, 15 is XV, meaning X + V = 10 + 5 = 15, which does not use subtractive notation, so 15 is not in the sequence.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..1952 (complete up to 3999)

Crossrefs

Cf. A061493.

Cf. A016897, 5n + 4 (first diverges after 39, as that sequence does not include 40, 41, 42, 43).

Programs

Maple

with(StringTools): for n from 1 to 300 do r:=convert(n,roman): if(Search("IV",r)>0 or Search("IX",r)>0 or Search("XL",r)>0 or Search("XC",r)>0 or Search("CD",r)>0 or Search("CM",r)>0)then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Mathematica

Select[Range[3999], StringContainsQ[RomanNumeral[#], {"IV", "IX", "XL", "XC", "CD", "CM"}] &] (* Michael De Vlieger, Aug 20 2024 *)

Python

def ok(n): return {"4", "9"} & set(str(n))
afull = [k for k in range(4000) if ok(k)] # Michael S. Branicky, Aug 20 2024