A119310 -id:A119310 - cp's OEIS frontend

A002963 Number of chisel strokes required for Roman numerals for n.

1, 2, 3, 3, 2, 3, 4, 5, 3, 2, 3, 4, 5, 5, 4, 5, 6, 7, 5, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 6, 7, 8, 9, 9, 8, 9, 10, 11, 9, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 2, 3, 4, 5, 5, 4, 5, 6, 7, 5, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 6, 7, 8, 9, 9, 8, 9, 10, 11, 9, 8, 9, 10, 11, 11, 10, 11, 12, 13, 11, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 2, 3, 4

Offset: 1

N. J. A. Sloane

Chisel strokes for numerals: I,1; V,2; X,2; L,2; C ( = < ),2; D,3; M,4.
For more about Roman numerals, see A006968.
a(A002964(n)) = n. - Reinhard Zumkeller, Apr 14 2013

Nathaniel Johnston, Table of n, a(n) for n = 1..3999
Eric Weisstein's World of Mathematics, Roman Numerals
Wikipedia, Roman numerals

Cf. A119310.

Cf. A061493, A093783.

a002963 = ch 0 . a061493 where
     ch s 0 = s
     ch s x = ch (s + [0,1,2,2,2,2,3,4] !! d') x'
              where  (x',d) = divMod x 10; d' = fromInteger d
-- Reinhard Zumkeller, Apr 14 2013

with(StringTools): A002963 := proc(n) local r: r:=convert(n, roman): return add(parse(SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll(r[j], "I", "1"), "V", "2"), "X", "2"), "L", "2"), "C", "2"), "D", "3"), "M", "4")), j=1..length(r)): end: seq(A002963(n), n=1..102); # Nathaniel Johnston, May 18 2011

a[n_] := Characters[ IntegerString[n, "Roman"]] /. {"I" -> 1, "V" -> 2, "X" -> 2, "L" -> 2, "C" -> 2, "D" -> 3, "M" -> 4} // Total; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Sep 10 2013 *)

{A002963(n, c=[1000, 4, 900, 6, 500, 3, 400, 5, 100, 2, 90, 4, 50, 2, 40, 4, 10, 2, 9, 3, 5, 2, 4, 3, 1, 1], s=0)= forstep(i=1, #c, 2, while(n>=c[i], n-=c[i]; s+=c[i+1])); s} \\ M. F. Hasler, Jul 27 2016

a002963 = lambda n: sum((d+1-(d==2))*(i%5)+(d+2-(d==1))*(i>4) if (i+1)%5 else 3+d+(d==2)*(i==9) for d,i in enumerate(map(int,str(n)[::-1])))
# Nicholas Stefan Georgescu, Feb 27 2023

More terms from David W. Wilson

Data double-checked by M. F. Hasler, Jul 27 2016

A036788 Length of Roman notation for n <= length of decimal representation.

Original entry on oeis.org

1, 5, 10, 11, 15, 20, 40, 50, 51, 55, 60, 90, 100, 101, 102, 104, 105, 106, 109, 110, 111, 115, 120, 140, 150, 151, 155, 160, 190, 200, 201, 205, 210, 250, 300, 400, 401, 405, 410, 450, 500, 501, 502, 504, 505, 506, 509, 510, 511, 515, 520, 540, 550, 551, 555

Offset: 1

N. J. A. Sloane

The Roman numeration system used here is the naive one taught in primary school. This sequence, like many others involving numeration systems, is neither well-defined nor interesting for large values of n. - N. J. A. Sloane, Jul 03 2008

			15 = XV has length 2 in both notations.

Nathaniel Johnston, Table of n, a(n) for n = 1..199 (complete up to 3999)
Paul Lewis, Roman numerals

Cf. A036786, A036787, A105269, A119310, A121305.

a036788 n = a036788_list !! (n-1)
a036788_list = [x | x <- [1..], a006968 x <= a055642 x]
-- Reinhard Zumkeller, Apr 20 2013

for n from 1 to 3999 do if(length(convert(n, roman)) <= length(n))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Select[Range[560],StringLength[IntegerString[#,"Roman"]]<= IntegerLength[ #]&] (* Harvey P. Dale, Dec 18 2011 *)

A006968(a(n)) <= A055642(a(n)). - Reinhard Zumkeller, Apr 20 2013

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Sep 25 2000

cp's OEIS Frontend

A002963 Number of chisel strokes required for Roman numerals for n.

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