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Number of letters in "old style" Roman numeral representation of n (e.g., IIII rather than IV).
6

%I #25 Oct 19 2017 17:27:29

%S 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,

%T 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,

%U 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

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

%C How is this sequence defined for large values? - _Charles R Greathouse IV_, Feb 01 2011

%C 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

%H Nathaniel Johnston, <a href="/A092196/b092196.txt">Table of n, a(n) for n = 0..3999</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Abacus">Abacus</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Soroban">Soroban</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Suanpan">Suanpan</a>

%H <a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a>

%e a(99)=10 because 99 is LXXXXVIIII.

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

%o (PARI) a(n)=vecsum(apply(v->(v\5)+(v%5), digits(n))); \\ _Andrew Howroyd_, Oct 19 2017

%Y Cf. A006968.

%K base,easy,nonn

%O 0,3

%A _Marc LeBrun_, Feb 24 2004

%E a(0)=0 prepended by _Andrew Howroyd_, Oct 19 2017