A105247 Product of digits of Roman Numerals.

1, 1, 1, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 50, 50, 50, 50, 50, 100, 100, 100, 100, 100, 500, 500, 500, 500, 500, 1000, 1000, 1000, 1000, 1000, 5000, 5000, 5000, 5000, 5000, 10000, 500, 500, 500, 500, 2500, 2500, 2500, 2500, 2500, 5000, 50, 50, 50, 50, 250

Offset: 1

Author

Jonathan Vos Post, Apr 14 2005

Keywords

• base
• easy
• fini
• nonn

Comments

New Roman Numerals A006968 (i.e., 4 = IV, not IIII). Related to sum of digits of n in Roman numeral representation A093783.

Examples

			a(3) = 1 because 3 = "III" and I*I*I = I = 1.
a(4) = 5 because 4 = "IV" and I*V = V = 5.
a(9) = 10 because 9 = "IX" and I*X = X = 10.
a(14) = 50 because 14 = "XIV" and X*I*V = L = 50.
a(19) = 100 because 19 = "XIX" and X*I*X = C = 100.
a(24) = 500 because 24 = "XXIV" and X*X*I*V = D = 500.
a(29) = 1000 because 29 = "XXIX" and X*X*I*X = M = 1000.
a(34) = 5000 because 34 = "XXXIV" and X*X*X*I*V = 5000.
a(39) = 10000 because 39 = "XXXIX" and X*X*X*I*X = myriad = 10000.
a(40) = 500 because 40 = "XL" and X*L = D = 500.
a(44) = 2500 because 44 = "XLIV" and X*L*I*V = MMD = 2500.
a(49) = 5000 because 49 = "XLIX" and X*L*I*X = 5000.
a(50) = 50 because 50 = L.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..3999
• Gerard Schildberger and Frank Ellermann, The numbers from 1 to 3999 expressed as Roman numerals.

Crossrefs

Cf. A006968, A093783.

Programs

Maple

with(StringTools): A105247 := proc(n) local r: r:=convert(n, roman): return mul(parse(SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll(r[j], "I", "1"), "V", "5"), "X", "10"), "L", "50"), "C", "100"), "D", "500"), "M", "1000")),j=1..length(r)): end: seq(A105247(n),n=1..54); # Nathaniel Johnston, May 18 2011