A006968 -id:A006968 - cp's OEIS frontend

A036742 Numbers <= 3999 sorted in Roman numeral lexicographic order.

100, 200, 300, 301, 302, 303, 304, 309, 350, 351, 352, 353, 354, 359, 355, 356, 357, 358, 360, 361, 362, 363, 364, 369, 365, 366, 367, 368, 370, 371, 372, 373, 374, 379, 375, 376, 377, 378, 380, 381, 382, 383, 384, 389, 385, 386, 387, 388, 305, 306, 307

Offset: 1

David W. Wilson

Beyond 3999 the numerals are not representable in ASCII and hence sorting becomes problematic. - Steven N. Severinghaus, Nov 17 2007

Steven N. Severinghaus, Table of n, a(n) for n = 1..3999

Cf. A006968, A036741, A036743.

A036742 := sort([seq(convert(n, roman), n=1..3999)], lexorder): seq(convert(A036742[n], arabic), n=1..51); # Nathaniel Johnston, May 18 2011

FromRomanNumeral[Sort[RomanNumeral[Range[3999]]]] (* Hans Havermann, May 06 2019; requires Mathematica 10.2+ *)

#!/bin/bash
# Requires Roman module:
# http://search.cpan.org/~chorny/Roman-1.20/lib/Roman.pm
perl -e 'use Roman; for(1..3999) { print roman($_)."
"; }' | sort | perl -ne 'use Roman; chomp; print arabic($_)."
"'
# Steven N. Severinghaus, Nov 17 2007

import roman
A36742=sorted(range(1,4000), key=roman.toRoman)
def A036742(n): return A36742[n-1] # M. F. Hasler, Aug 16 2025

A280913 Number of dots in International Morse numeral representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2

Offset: 0

Indranil Ghosh, Jan 10 2017

The Morse Code is written in current ITU standard.

For the number of dashes see A280916.

			For n = 4, the Morse numeral representation of 4 is "....-" i.e., 4 dots. So, a(4) = 4.
For n = 26, the Morse numeral representation of 26 is "..--- -...." i.e, 6 dots. So, a(26) = 6.

Indranil Ghosh, Table of n, a(n) for n = 0..10000
Wikipedia, Morse code
Wikipedia, International Telecommunication Union

Cf. A060109 (Morse code for n), A280916 (number of dashes), A268643 (number of '1's in n).

Cf. A006968, A278182.

Table[Total[IntegerDigits[n]/.{6->4,7->3,8->2,9->1}],{n,0,120}] (* Harvey P. Dale, Feb 06 2020 *)

apply( {A280913(n)=if(n>9,self()(n\10)+self()(n%10), 5-abs(n-5))}, [0..88]) \\ M. F. Hasler, Jun 22 2020

M={"1":".----","2":"..---","3":"...--","4":"....-","5":".....","6":"-....","7":"--...","8":"---..","9":"----.","0":"-----"}
def A280913(n):
    z="".join(M[i] for i in str(n))
    return z.count(".")
print([A280913(n) for n in range(101)])

a(n) = A268643(A060109(n)) = floor(1+n/10)*5 - A280916(n) = a(floor(n/10)) + a(n%10) if n > 9 or min(n, 10-n) = 5 - |5 - n| otherwise, where % is the modulo (remainder) operator. - M. F. Hasler, Jun 22 2020

A280916 Number of dashes in International Morse numeral representation of n.

Original entry on oeis.org

5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 14

Offset: 0

Indranil Ghosh, Jan 10 2017

The Morse Code is written in current ITU standard.

			For n = 4, the Morse numeral representation of 4 is "....-" i.e., 1 dash. So, a(4) = 1.
For n = 26, the Morse numeral representation of 26 is "..--- -...." i.e, 4 dashes. So, a(26) = 4.

Indranil Ghosh, Table of n, a(n) for n = 0..10000
Wikipedia, Morse code
Wikipedia, International Telecommunication Union

Cf. A060109 (Morse code of n), A280913 (number of dots).

Cf. A006968, A278182 (for Roman resp. Maya representation of n).

Array[Total@ Map[Abs[# - 5] &, IntegerDigits[#]] &, 101, 0] (* Michael De Vlieger, Jun 28 2020 *)

apply( {A280916(n)=if(n>9, self()(n\10)+self()(n%10), abs(n-5))}, [0..88]) \\ M. F. Hasler, Jun 22 2020

M={"1":".----","2":"..---","3":"...--","4":"....-","5":".....","6":"-....","7":"--...","8":"---..","9":"----.","0":"-----"}
def A280916(n):
    z="".join(M[i] for i in str(n))
    return z.count("-")
print([A280916(n) for n in range(100)])

a(n) = A316863(A060109(n)) = floor(1+n/10)*5 - A280913(n) = a(floor(n/10)) + a(n%10) if n > 9 or |5 - n| otherwise, where % is the modulo (remainder) operator. - M. F. Hasler, Jun 22 2020

A093783 Sum of digits of n in Roman numeral representation.

Original entry on oeis.org

1, 2, 3, 6, 5, 6, 7, 8, 11, 10, 11, 12, 13, 16, 15, 16, 17, 18, 21, 20, 21, 22, 23, 26, 25, 26, 27, 28, 31, 30, 31, 32, 33, 36, 35, 36, 37, 38, 41, 60, 61, 62, 63, 66, 65, 66, 67, 68, 71, 50, 51, 52, 53, 56, 55, 56, 57, 58, 61, 60, 61, 62, 63, 66, 65, 66, 67, 68

Offset: 1

Reinhard Zumkeller, May 17 2004

			n=42 == XLII: a(42) = 'X' + 'L' + 'I' + 'I' = 10+50+1+1 = 62.

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

Cf. A007953, A057226, A006968.

Cf. A061493, A002963.

a093783 n = q 0 $ a061493 n where
     q s 0 = s
     q s x = q (s + [0,1,5,10,50,100,500,1000] !! d') x'
             where  (x',d) = divMod x 10; d' = fromInteger d
-- Reinhard Zumkeller, Apr 14 2013
(HP 49G calculator)
::
  CK1&Dispatch
  # FF
  ::
    FPTR2 ^DupQIsZero?
    caseSIZEERR
    FPTR2 ^Z>S
    Z0_
    SWAP
    DUPLEN$
    ZERO_DO
    DUP
    ISTOP-INDEX
    SUB$1#
    BINT48
    #-
    BINT4
    OVER#=
    OVER
    BINT9
    #=
    OR
    IT
    #2+
    FPTR2 ^#>Z
    Z10_
    INDEX@
    FPTR2 ^RP#
    FPTR2 ^RMULText
    ROT
    FPTR2 ^RADDext
    SWAPLOOP
    DROP
  ;
;
Gerald Hillier, Sep 08 2015

A093783 := proc(n) local r: r:=convert(n, roman): return add(convert(r[j], arabic), j=1..length(r)): end: seq(A093783(n), n=1..68); # Nathaniel Johnston, May 18 2011

Total[#2 FromRomanNumeral[#1] & @@@ Tally[Characters@ RomanNumeral@ #]] & /@ Range@ 68 (* Michael De Vlieger, Sep 08 2015, Version 10.2 *)

A105447 Positive integers whose representation as Roman Fibonacci numbers has exactly two symbols.

Original entry on oeis.org

4, 6, 7, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 29, 31, 32, 33, 35, 36, 37, 39, 42, 47, 50, 52, 53, 54, 56, 57, 58, 60, 63, 68, 76, 81, 84, 86, 87, 88, 90, 91, 92, 94, 97, 102, 110, 123, 131, 139, 141, 142, 143, 145, 146, 147, 149, 152, 157

Offset: 1

Jonathan Vos Post, Apr 09 2005

			In Roman Fibonacci number representation:
4 = "22", 6 = "33", 7 = "52", 9 = "81", 10 = "55", 11 = "83", 12 = "1A",
14 = "A1", 15 = "A2", 16 = "88", 18 = "3B", 19 = "2B", 20 = "1B", ...
143 = "1F", 145 = "F1", 146 = "F2", 147 = "F3", 149 = "F5", 152 = "F8".

Cf. A000045, A006968, A105446, A105448-A105455.

a(n) is an element of A105447 iff A105446(n) = 2. a(n) is the sum or difference of two Fibonacci numbers A000045 and a(n) is not itself a Fibonacci number A000045.

A105448 Positive integers whose representation as Roman Fibonacci numbers has exactly three symbols.

Original entry on oeis.org

17, 25, 27, 28, 30, 38, 40, 41, 43, 44, 45, 46, 48, 49, 51, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 82, 83, 85, 93, 95, 96, 98, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111, 112, 113, 115, 118, 124, 125, 126, 128, 132, 133, 134, 136, 140

Offset: 1

Jonathan Vos Post, Apr 09 2005

A105446 gives the number of symbols in Roman Fibonacci numbers. A105447 gives positive integers whose representation as Roman Fibonacci numbers has exactly two symbols. A105449 gives positive integers whose representation as Roman Fibonacci numbers has exactly four symbols. A105450 gives positive integers whose representation as Roman Fibonacci numbers has exactly five symbols.

			In Roman Fibonacci number representation:
17 = "A22", 25 = "B22", 27 = "AA1", 28 = "AA2", 30 = "B81", 38 = "C22", 40 = "C33", 41 = "C52", 43 = "BB1", 44 = "BB2", 45 = "BB3", 46 = "1CA", 48 = "CA1", ..., 155 = "2FA", 156 = "1FA", 158 = "FA1", 159 = "FA2", 160 = "FA3".

Cf. A000045, A006968, A105446, A105447, A105449-A105455.

a(n) is an element of A105447 iff A105446(n) = 3.

A105449 Positive integers whose representation as Roman Fibonacci numbers has exactly four symbols.

Original entry on oeis.org

80, 106, 114, 116, 117, 119, 120, 121, 122, 127, 129, 130, 135, 137, 138

Offset: 1

Jonathan Vos Post, Apr 09 2005

A105446 gives the number of symbols in Roman Fibonacci numbers. A105447 gives positive integers whose representation as Roman Fibonacci numbers has exactly two symbols. A105448 gives positive integers whose representation as Roman Fibonacci numbers has exactly three symbols. A105450 gives positive integers whose representation as Roman Fibonacci numbers has exactly five symbols.

			In Roman Fibonacci number representation:
80 = "DB22", 106 = "EA22", 114 = "DD22", 116 = "DD33", 117 = "DD52", 119 = "DD81", 120 = "DD55", 121 = "DD2A", 122 = "DD1A", 127 = "BF22", 129 = "BF33", 130 = "BF52", 135 = "AF22", 137 = "AF33", 138 = "AF52".

Cf. A000045, A006968, A105446-A105448, A105450-A105455.

a(n) is an element of A105449 iff A105446(n) = 4.

A160676 Numbers k such that k and 2k use the same number of characters when expressed in Roman numerals.

Original entry on oeis.org

2, 5, 7, 13, 18, 20, 22, 31, 36, 46, 50, 52, 55, 57, 63, 68, 70, 72, 81, 86, 95, 97, 103, 108, 123, 126, 130, 132, 135, 137, 145, 147, 153, 158, 173, 176, 180, 182, 185, 187, 198, 200, 202, 205, 207, 213, 218, 220, 222, 231, 236, 246, 254, 261, 266, 274

Offset: 1

Claudio Meller, May 23 2009

Example: 2 and its double 4 both need two characters in Roman numerals: 2=II, 4=IV. Also 5=V, 10=X; 7=VII, 14=XIV.

Nathaniel Johnston, Table of n, a(n) for n = 1..503 (complete up to 3999)
Eric Weisstein's World of Mathematics, Roman Numerals
Wikipedia, Roman numerals

Cf. A006968. - Jonathan Vos Post, May 24 2009

a160676 n = a160676_list !! (n-1)
a160676_list = filter (\x -> a006968 x == a006968 (2 * x)) [1..]
-- Reinhard Zumkeller, Apr 14 2013

for n from 1 to 3999 do if(length(convert(n, roman)) = length(convert(2*n, roman)))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Select[Range[300],StringLength[RomanNumeral[#]]==StringLength[ RomanNumeral[ 2 #]]&] (* Harvey P. Dale, Apr 29 2022 *)

{n: A006968(n) = A006968(2n)}. - Jonathan Vos Post, May 24 2009

A160677 Numbers k such that k, 2k and 3k use the same number of characters when expressed in Roman numerals.

Original entry on oeis.org

2, 7, 20, 22, 36, 70, 72, 97, 153, 200, 202, 207, 220, 222, 236, 315, 351, 360, 362, 379, 448, 653, 700, 702, 707, 720, 722, 736, 871, 970, 972, 997, 1035, 1087, 1177, 1235, 1267, 1350, 1352, 1357, 1386, 1537, 1677, 1735, 1767, 1818, 1836, 1870, 1872, 1897

Offset: 1

Claudio Meller, May 23 2009, May 24 2009

= II, 4 = IV, 6 = VI;
= VII, 14 = XIV, 21 = XXI;
= XX, 40 = XL, 60 = LX.

Nathaniel Johnston, Table of n, a(n) for n = 1..57 (complete up to 3999)

Cf. A006968.

for n from 1 to 3999 do if(length(convert(n, roman)) = length(convert(2*n, roman)) and length(convert(n, roman)) = length(convert(3*n, roman)))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Extended by Nathaniel Johnston, May 18 2011

A199921 Number of Roman numerals < 4000 with n letters.

Original entry on oeis.org

7, 31, 93, 215, 389, 573, 691, 691, 573, 389, 215, 93, 31, 7, 1

Offset: 1

Martin Renner, Nov 12 2011

Note that the sequence is completely symmetrical with the addition of the single (notional) Roman string of length zero. - Ian Duff, Jun 27 2017

			a(1) = 7, since there are the seven one-letter roman numerals I, V, X, L, C, D, M.
a(15) = 1, since there is one fifteen-letter roman numeral MMMDCCCLXXXVIII.

Eric Weisstein's World of Mathematics, Roman Numerals.
Wikipedia, Roman numerals

Cf. A003587, A006968.

Cf. A055642, A061493.

import Data.List (group, sort)
a199921 n = a199921_list !! (n-1)
a199921_list = map length $ group $ sort $ map (a055642 . a061493) [1..3999]
-- Reinhard Zumkeller, Apr 14 2013

for i from 1 to 15 do L[i]:={}: od: for n from 1 to 3999 do L[length(convert(n,roman))]:={op(L[length(convert(n,roman))]),n}; od:
seq(nops(L[i]),i=1..15); # Martin Renner, Nov 13 2011

romanLetterCount = Table[0, {15}]; j = 1; While[j < 4000, romanLetterCount[[StringLength[IntegerString[j, "Roman"]]]]++; j++]; romanLetterCount (* Alonso del Arte, Nov 12 2011 *)
Rest[BinCounts[StringLength[RomanNumeral[Range[3999]]]]] (* Paolo Xausa, Mar 19 2024 *)

cp's OEIS Frontend

A036742 Numbers <= 3999 sorted in Roman numeral lexicographic order.

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A280913 Number of dots in International Morse numeral representation of n.

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A280916 Number of dashes in International Morse numeral representation of n.

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A093783 Sum of digits of n in Roman numeral representation.

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A105447 Positive integers whose representation as Roman Fibonacci numbers has exactly two symbols.

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A105448 Positive integers whose representation as Roman Fibonacci numbers has exactly three symbols.

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A105449 Positive integers whose representation as Roman Fibonacci numbers has exactly four symbols.

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A160676 Numbers k such that k and 2k use the same number of characters when expressed in Roman numerals.

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