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

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

Author

Indranil Ghosh, Jan 10 2017

Keywords

• nonn
• base

Comments

The Morse Code is written in current ITU standard.

Examples

			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.
		

Links

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

Crossrefs

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

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

Programs

Mathematica

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

PARI

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

Python

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)])

Formula

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