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

1,2

Comments

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..3999

Eric Weisstein's World of Mathematics, Roman Numerals

Wikipedia, Roman numerals

Maple

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

Mathematica

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 *)

Prog

(Haskell)
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
(PARI) {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
(Python)
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

Crossrefs

Cf. A119310.

Cf. A061493, A093783.

Sequence in context: A107918 A242392 A382191 * A046677 A382871 A283104

Adjacent sequences: A002960 A002961 A002962 * A002964 A002965 A002966

Keyword

base,easy,nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

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

Status

approved