login
A269624
Length of the shortest generalized Roman numeral representation of n.
0
1, 2, 3, 2, 1, 2, 3, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 4, 3, 2, 3, 4, 5, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 3, 4, 5, 4, 3, 2, 3, 4, 4, 3, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 4, 3, 2, 3, 4, 5, 4, 3, 4, 5, 5, 4, 3, 4, 5, 6, 5, 4, 5, 6, 5, 4, 3, 4, 5, 5, 4, 3, 4, 5, 4, 3, 2, 3, 4, 4, 3, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2
OFFSET
1,2
COMMENTS
In generalized Roman numerals, any sequence of characters from I,V,X,L,C,D,M can be interpreted uniquely as an (possibly negative) integer. So for instance IIX = 10 - 2 = 8 and IVXX = 20 - (5 - 1) = 16. The rule is: 1. First look for the first instance of the largest character in the string. 2. Everything preceding it is recursively evaluated and subtracted from the value. 3. Everything after it is recursively evaluated and added to the value.
EXAMPLE
For numbers up to 50, one possible shortest representation is: I, II, III, IV, V, VI, VII, IIX, IX, X, XI, XII, XIII, XIV, XV, XVI, XVII, XIIX, XIX, XX, XXI, XXII, XXIII, XXIV, XXV, XXVI, XXVII, XXIIX, XXIX, XXX, XXXI, XXXII, XVIIL, XVIL, XVL, XVLI, XVLII, XIIL, XIL, XL, XLI, XLII, VIIL, VIL, VL, VLI, VLII, IIL, IL, L.
CROSSREFS
Cf. A006968.
Sequence in context: A320858 A304111 A030314 * A098236 A152978 A118121
KEYWORD
nonn,base
AUTHOR
David Spies, Mar 01 2016
STATUS
approved