cp's OEIS Frontend

A082763 Roman numeral contains an asymmetric symbol (L).

%I A082763 #20 Feb 16 2025 08:32:49
%S A082763 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
%T A082763 63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
%U A082763 86,87,88,89,140,141,142,143,144,145,146,147,148,149,150,151,152
%N A082763 Roman numeral contains an asymmetric symbol (L).
%C A082763 I,V,X,C,D,M - and even the vinculum (bar) and apostrophus (backwards "C") - are each symmetric: horizontally, vertically, or both.
%C A082763 Numbers containing a 4 when decimally encoded with A061493. - _Reinhard Zumkeller_, Apr 14 2013
%H A082763 Nathaniel Johnston, <a href="/A082763/b082763.txt">Table of n, a(n) for n = 1..2000</a> (complete up to 3999)
%H A082763 Gerard Schildberger, <a href="/A006968/a006968.txt">The first 3999 numbers in Roman numerals</a>
%H A082763 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RomanNumeral.html">Roman Numeral.</a>
%F A082763 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].
%e A082763 40 = XL, 89 = LXXXIX, 140 = CXL.
%p A082763 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
%t A082763 Select[Range[200],StringCases[RomanNumeral[#],"L"]!={}&] (* _Harvey P. Dale_, Jun 10 2023 *)
%o A082763 (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),","))
%o A082763 (Haskell)
%o A082763 a082763 n = a082763_list !! (n-1)
%o A082763 a082763_list = filter (containsL . a061493) [1..3999] where
%o A082763    containsL x = d == 4 || x > 0 && containsL x' where
%o A082763                  (x',d) = divMod x 10
%o A082763 -- _Reinhard Zumkeller_, Apr 14 2013
%Y A082763 Cf. A006968 (Roman numerals main entry), A078715 (Palindromic Roman numerals).
%K A082763 base,easy,nonn
%O A082763 1,1
%A A082763 _Rick L. Shepherd_, May 21 2003