A105417 Numbers that are pandigital in Roman numerals, using each of the symbols I, V, X, L, C, D and M at least once.

1444, 1446, 1447, 1448, 1464, 1466, 1467, 1468, 1474, 1476, 1477, 1478, 1484, 1486, 1487, 1488, 1644, 1646, 1647, 1648, 1664, 1666, 1667, 1668, 1674, 1676, 1677, 1678, 1684, 1686, 1687, 1688, 1744, 1746, 1747, 1748, 1764, 1766, 1767, 1768, 1774, 1776

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

Cf. A061493, A105416.

Sequence in context: A252224 A221872 A251842 * A105416 A348740 A368191

Adjacent sequences: A105414 A105415 A105416 * A105418 A105419 A105420

Keyword

base,fini,full,easy,nonn

Author

Robert Happelberg (roberthappelberg(AT)yahoo.com), Apr 06 2005

Status

approved