A036787 Length of Roman notation for n = length of decimal representation.

1, 5, 11, 15, 20, 40, 51, 55, 60, 90, 102, 104, 106, 109, 111, 115, 120, 140, 151, 155, 160, 190, 201, 205, 210, 250, 300, 401, 405, 410, 450, 502, 504, 506, 509, 511, 515, 520, 540, 551, 555, 560, 590, 601, 605, 610, 650, 700, 901, 905, 910, 950, 1003, 1007

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Examples

			15 = XV has length 2 in both notations.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..144 (complete up to 3999)

Crossrefs

Cf. A036786, A036788.

Programs

Haskell

a036787 n = a036787_list !! (n-1)
a036787_list = [x | x <- [1..], a006968 x == a055642 x]
-- Reinhard Zumkeller, Apr 20 2013

Maple

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

Mathematica

Select[Range[1100],StringLength[IntegerString[#,"Roman"]] == IntegerLength[ #]&] (* Harvey P. Dale, Jul 25 2011 *)

PARI

is_A036787(n)=#Str(n)==#Str(A061493(n)) \\ M. F. Hasler, Jan 12 2015

Formula

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

Extensions

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