OFFSET
1,1
COMMENTS
Contains A105416. The largest member of this sequence is 3888, MMMDCCCLXXXVIII.
From Daniel Forgues, Jul 31 2011: (Start)
There are 192 = 3 * 4^3 pandigital Roman numerals:
3 ways to start: M*, MM*, MMM* (since no Roman numeral stood for 5000)
4 ways for the hundreds: *CD*, *DC*, *DCC*, *DCCC*
4 ways for the decades: *XL*, *LX*, *LXX*, *LXXX*
4 ways for the units: *IV, *VI, *VII, *VIII (End)
Equivalently, numbers of the form abcd with 1 <= a <= 3 and b,c,d in {4,6,7,8}. - M. F. Hasler, Jul 10 2018
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..192 (full sequence)
FORMULA
A006968(a(n)) >= 7. - Reinhard Zumkeller, Apr 14 2013
EXAMPLE
a(3) = 1447 because its Roman numeral representation, MCDXLVII, uses each of the symbols V, X, L, C, D and M once and the symbol I twice.
MAPLE
with(StringTools): for n from 1 to 3999 do r:=convert(n, roman): if Search("I", r) > 0 and Search("V", r) > 0 and Search("X", r) > 0 and Search("L", r) > 0 and Search("C", r) > 0 and Search("D", r) > 0 and Search("M", r) > 0 then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011
A105417 := select(n->nops(convert(convert(n, roman), set))=7, `$`(3888)) # M. F. Hasler, Jul 10 2018
MATHEMATICA
Select[Range[900, 1776], ContainsAll[Characters[RomanNumeral[#]], {"M", "C", "D", "X", "L", "I", "V"}]&] (* James C. McMahon, Jan 24 2024 *)
PROG
(Haskell)
import Data.List (nub, sort)
a105417 n = a105417_list !! (n-1)
a105417_list = filter ((== "1234567") . sort . nub . show . a061493) [1..3999]
-- Reinhard Zumkeller, Apr 14 2013
(PARI) A105417=vector(192, i, fromdigits(apply(d->d-!d, digits(i+63, 4)))+555) \\ M. F. Hasler, Jul 10 2018
CROSSREFS
KEYWORD
base,fini,full,easy,nonn
AUTHOR
Robert Happelberg (roberthappelberg(AT)yahoo.com), Apr 06 2005
STATUS
approved