A006968 Number of letters in Roman numeral representation of n. (Formerly M0417)

1, 2, 3, 2, 1, 2, 3, 4, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 4, 3, 4, 5, 6, 5, 4, 5, 6, 7, 5, 2, 3, 4, 5, 4, 3, 4, 5, 6, 4, 1, 2, 3, 4, 3, 2, 3, 4, 5, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 4, 3, 4, 5, 6, 5, 4, 5, 6, 7, 5, 4, 5, 6, 7, 6, 5, 6, 7, 8, 6, 2, 3, 4, 5, 4, 3, 4, 5, 6, 4, 1, 2, 3, 4, 3, 2

Offset

1,2

Comments

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

See A078715 for a discussion on the Roman 4M-problem. - Reinhard Zumkeller, Apr 14 2013

The sequence can be considered to be defined via the formula (as A055642 o A061493), so the question is to be posed in A061493, not here. - M. F. Hasler, Jan 12 2015

References

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 60.

Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file. (Science Section).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

Rec.puzzles, Archive

Gerard Schildberger, The first 3999 numbers in Roman numerals

Eric Weisstein's World of Mathematics, Roman Numerals

Wikipedia, Roman numerals

Index entries for sequences related to number of letters in n

Formula

A006968 = A055642 o A061493, i.e., a(n) = A055642(A061493(n)). - M. F. Hasler, Jan 11 2015

Maple

A006968 := proc(n) return length(convert(n, roman)): end: seq(A006968(n), n=1..105); # Nathaniel Johnston, May 18 2011

Mathematica

a[n_] := StringLength[ IntegerString[ n, "Roman"]]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Dec 27 2011 *)

Prog

(R) as.roman(1 :1024) # N. J. A. Sloane, Aug 23 2009
(Haskell)
a006968 = lenRom 3 where
   lenRom 0 z = z
   lenRom p z = [0, 1, 2, 3, 2, 1, 2, 3, 4, 2] !! m + lenRom (p - 1) z'
                where (z', m) = divMod z 10
-- Reinhard Zumkeller, Apr 14 2013
(PARI) A006968(n)=#Str(A061493(n)) \\ M. F. Hasler, Jan 11 2015
(Python)
def f(s, k):
    return s[:2] if k==4 else (s[1]*(k>=5)+s[0]*(k%5) if k<9 else s[0]+s[2])
def a(n):
    m, c, x, i = n//1000, (n%1000)//100, (n%100)//10, n%10
    return len("M"*m + f("CDM", c) + f("XLC", x) + f("IVX", i))
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Mar 03 2024

Crossrefs

Cf. A002963, A036746, A036786, A036787, A036788, A061493, A092196, A160676, A160677, A199921.

Sequence in context: A098236 A152978 A118121 * A058207 A105969 A275892

Adjacent sequences: A006965 A006966 A006967 * A006969 A006970 A006971

Keyword

nonn,base,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Eric W. Weisstein

Status

approved