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
Examples
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.
Links
- Nathaniel Johnston, Table of n, a(n) for n = 1..192 (full sequence)
Programs
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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
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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 *) -
PARI
A105417=vector(192,i,fromdigits(apply(d->d-!d,digits(i+63,4)))+555) \\ M. F. Hasler, Jul 10 2018
Formula
A006968(a(n)) >= 7. - Reinhard Zumkeller, Apr 14 2013
Comments