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
KEYWORD
base,easy,nonn
AUTHOR
Rick L. Shepherd, May 21 2003
STATUS
approved