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

1,4

Comments

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

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.

Example

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.

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

Crossrefs

Cf. A006968, A093783.

Sequence in context: A291497 A241154 A094636 * A245357 A001735 A245101

Adjacent sequences: A105244 A105245 A105246 * A105248 A105249 A105250

Keyword

base,easy,fini,nonn

Author

Jonathan Vos Post, Apr 14 2005

Status

approved