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

1,2

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.

Links

Table of n, a(n) for n=1..105.

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

Adjacent sequences: A269621 A269622 A269623 * A269625 A269626 A269627

Keyword

nonn,base

Author

David Spies, Mar 01 2016

Status

approved