A120433 Numbers n with property that the Roman numeral for n 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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Sequence in context: A190086 A313114 A313115 * A277601 A172324 A313116

Adjacent sequences: A120430 A120431 A120432 * A120434 A120435 A120436

Keyword

base,easy,nonn

Author

Christian Amet, Jul 13 2006

Status

approved