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

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

Author

Indranil Ghosh, Jan 10 2017

Keywords

• nonn
• base

Comments

The Morse Code is written in current ITU standard.

For the number of dashes see A280916.

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A006968, A278182.

Programs

Mathematica

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

PARI

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

Python

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)])

Formula

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