A269624 Length of the shortest generalized Roman numeral representation of n.

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

Author

David Spies, Mar 01 2016

Keywords

• nonn
• base

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.

Examples

			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.