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A082763 Roman numeral contains an asymmetric symbol (L). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified September 26 03:40 EDT 2022. Contains 356986 sequences. (Running on oeis4.)