A092196 Number of letters in "old style" Roman numeral representation of n (e.g., IIII rather than IV).

0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 2

Offset: 0

Author

Marc LeBrun, Feb 24 2004

Keywords

• base
• easy
• nonn

Comments

How is this sequence defined for large values? - Charles R Greathouse IV, Feb 01 2011

Also, number of abacus pieces moved (i.e., differing from their initial positions) for the expression of n on a Chinese abacus. A Chinese abacus is also called "suanpan"(CN), "soroban"(JP). - FUNG Cheok Yin, Aug 08 2017

Examples

			a(99)=10 because 99 is LXXXXVIIII.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..3999
• Wikipedia, Abacus
• Wikipedia, Soroban
• Wikipedia, Suanpan
• Index entries for sequences related to number of letters in n

Crossrefs

Cf. A006968.

Programs

Maple

A092196 := proc(n) return length(convert(n, roman, period=early)): end: seq(A092196(n),n=1..105); # Nathaniel Johnston, May 18 2011

PARI

a(n)=vecsum(apply(v->(v\5)+(v%5), digits(n))); \\ Andrew Howroyd, Oct 19 2017

Extensions

a(0)=0 prepended by Andrew Howroyd, Oct 19 2017