Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #34 Jan 25 2024 00:58:02
%S 1444,1446,1447,1448,1464,1466,1467,1468,1474,1476,1477,1478,1484,
%T 1486,1487,1488,1644,1646,1647,1648,1664,1666,1667,1668,1674,1676,
%U 1677,1678,1684,1686,1687,1688,1744,1746,1747,1748,1764,1766,1767,1768,1774,1776
%N Numbers that are pandigital in Roman numerals, using each of the symbols I, V, X, L, C, D and M at least once.
%C Contains A105416. The largest member of this sequence is 3888, MMMDCCCLXXXVIII.
%C From _Daniel Forgues_, Jul 31 2011: (Start)
%C There are 192 = 3 * 4^3 pandigital Roman numerals:
%C 3 ways to start: M*, MM*, MMM* (since no Roman numeral stood for 5000)
%C 4 ways for the hundreds: *CD*, *DC*, *DCC*, *DCCC*
%C 4 ways for the decades: *XL*, *LX*, *LXX*, *LXXX*
%C 4 ways for the units: *IV, *VI, *VII, *VIII (End)
%C 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 Nathaniel Johnston, <a href="/A105417/b105417.txt">Table of n, a(n) for n = 1..192</a> (full sequence)
%F A006968(a(n)) >= 7. - _Reinhard Zumkeller_, Apr 14 2013
%e 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 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 := select(n->nops(convert(convert(n,roman),set))=7, `$`(3888)) # _M. F. Hasler_, Jul 10 2018
%t Select[Range[900,1776],ContainsAll[Characters[RomanNumeral[#]],{"M","C","D","X","L","I","V"}]&] (* _James C. McMahon_, Jan 24 2024 *)
%o (Haskell)
%o import Data.List (nub, sort)
%o a105417 n = a105417_list !! (n-1)
%o a105417_list = filter ((== "1234567") . sort . nub . show . a061493) [1..3999]
%o -- _Reinhard Zumkeller_, Apr 14 2013
%o (PARI) A105417=vector(192,i,fromdigits(apply(d->d-!d,digits(i+63,4)))+555) \\ _M. F. Hasler_, Jul 10 2018
%Y Cf. A061493, A105416.
%K base,fini,full,easy,nonn
%O 1,1
%A Robert Happelberg (roberthappelberg(AT)yahoo.com), Apr 06 2005