Template:Sequence of the Day for July 30

Intended for: July 30, 2012

Timetable

• First draft entered by Alonso del Arte on April 30, 2011 ✓
• Draft reviewed by Alonso del Arte on July 28, 2011 ✓
• Draft approved by Daniel Forgues on July 30, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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

{ MCDXLIV, MCDXLVI, MCDXLVII, MCDXLVIII, MCDLXIV, MCDLXVI, MCDLXVII, ... }

We consider the largest member of this sequence to be MMMDCCCLXXXVIII, since none of the many systems to cope with greater numbers became standard prior to Roman numerals being displaced by modern numerals.

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.

Note that the Roman numeral representation of numbers is not admissible in the OEIS, thus the decimal representation of those numbers is used in A105417.