

A105247


Product of digits of Roman Numerals.


1



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
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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



