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%I A105417 #34 Jan 25 2024 00:58:02
%S A105417 1444,1446,1447,1448,1464,1466,1467,1468,1474,1476,1477,1478,1484,
%T A105417 1486,1487,1488,1644,1646,1647,1648,1664,1666,1667,1668,1674,1676,
%U A105417 1677,1678,1684,1686,1687,1688,1744,1746,1747,1748,1764,1766,1767,1768,1774,1776
%N A105417 Numbers that are pandigital in Roman numerals, using each of the symbols I, V, X, L, C, D and M at least once.
%C A105417 Contains A105416. The largest member of this sequence is 3888, MMMDCCCLXXXVIII.
%C A105417 From _Daniel Forgues_, Jul 31 2011: (Start)
%C A105417   There are 192 = 3 * 4^3 pandigital Roman numerals:
%C A105417   3 ways to start: M*, MM*, MMM* (since no Roman numeral stood for 5000)
%C A105417   4 ways for the hundreds: *CD*, *DC*, *DCC*, *DCCC*
%C A105417   4 ways for the decades: *XL*, *LX*, *LXX*, *LXXX*
%C A105417   4 ways for the units: *IV, *VI, *VII, *VIII (End)
%C A105417 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
%H A105417 Nathaniel Johnston, <a href="/A105417/b105417.txt">Table of n, a(n) for n = 1..192</a> (full sequence)
%F A105417 A006968(a(n)) >= 7. - _Reinhard Zumkeller_, Apr 14 2013
%e A105417 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.
%p A105417 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
%p A105417 A105417 := select(n->nops(convert(convert(n,roman),set))=7, `$`(3888)) # _M. F. Hasler_, Jul 10 2018
%t A105417 Select[Range[900,1776],ContainsAll[Characters[RomanNumeral[#]],{"M","C","D","X","L","I","V"}]&] (* _James C. McMahon_, Jan 24 2024 *)
%o A105417 (Haskell)
%o A105417 import Data.List (nub, sort)
%o A105417 a105417 n = a105417_list !! (n-1)
%o A105417 a105417_list = filter ((== "1234567") . sort . nub . show . a061493) [1..3999]
%o A105417 -- _Reinhard Zumkeller_, Apr 14 2013
%o A105417 (PARI) A105417=vector(192,i,fromdigits(apply(d->d-!d,digits(i+63,4)))+555) \\ _M. F. Hasler_, Jul 10 2018
%Y A105417 Cf. A061493, A105416.
%K A105417 base,fini,full,easy,nonn
%O A105417 1,1
%A A105417 Robert Happelberg (roberthappelberg(AT)yahoo.com), Apr 06 2005

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