A082763 Roman numeral contains an asymmetric symbol (L).

40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152

Offset

1,1

Comments

I,V,X,C,D,M - and even the vinculum (bar) and apostrophus (backwards "C") - are each symmetric: horizontally, vertically, or both.

Numbers containing a 4 when decimally encoded with A061493. - Reinhard Zumkeller, Apr 14 2013

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..2000 (complete up to 3999)

Gerard Schildberger, The first 3999 numbers in Roman numerals

Eric Weisstein's World of Mathematics, Roman Numeral.

Formula

a(n+50) = a(n) + 100 for n >= 1 [a(n+L) = a(n) + C for n >= I], a(1) = 40 [a(I) = XL], a(n+1) = a(n) + 1 for 1 <= n <= 49 [a(n+I) = a(n) + I for I <= n <= XLIX]; so a(n) = floor((n-1)/50)*100 + 40 + ((n-1)(mod 50)) for n >= 1 [a(n) = floor((n-I)/L)*C + XL + ((n-I)(mod L)) for n >= I].

Example

40 = XL, 89 = LXXXIX, 140 = CXL.

Maple

with(StringTools): for n from 1 to 152 do if(Search("L", convert(n, roman)) > 0)then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Mathematica

Select[Range[200], StringCases[RomanNumeral[#], "L"]!={}&] (* Harvey P. Dale, Jun 10 2023 *)

Prog

(PARI) /* "%" use below is actually identical to lift(Mod(n-1, 50)) */ /* (n-1)<backslash>50 could be used for integer division below */ /* instead of floor, but the OEIS sometimes loses <backslash> */ /* characters depending upon where on a submitted line they are. */ a(n)=floor((n-1)/50)*100+40+(n-1)%50 for(n=1, 125, print1(a(n), ", "))
(Haskell)
a082763 n = a082763_list !! (n-1)
a082763_list = filter (containsL . a061493) [1..3999] where
   containsL x = d == 4 || x > 0 && containsL x' where
                 (x', d) = divMod x 10
-- Reinhard Zumkeller, Apr 14 2013

Crossrefs

Cf. A006968 (Roman numerals main entry), A078715 (Palindromic Roman numerals).

Sequence in context: A023482 A273770 A165861 * A007634 A228184 A128843

Adjacent sequences: A082760 A082761 A082762 * A082764 A082765 A082766

Keyword

base,easy,nonn

Author

Rick L. Shepherd, May 21 2003

Status

approved