A321332 Duration of Morse code representation of n.

19, 17, 15, 13, 11, 9, 11, 13, 15, 17, 39, 37, 35, 33, 31, 29, 31, 33, 35, 37, 37, 35, 33, 31, 29, 27, 29, 31, 33, 35, 35, 33, 31, 29, 27, 25, 27, 29, 31, 33, 33, 31, 29, 27, 25, 23, 25, 27, 29, 31, 31, 29, 27, 25, 23, 21, 23, 25, 27, 29, 33, 31, 29, 27, 25, 23, 25, 27, 29, 31, 35, 33, 31, 29, 27, 25, 27

Offset

0,1

Comments

In the Morse Code (ITU) the time unit is the duration of a dot. A dash has duration of 3 dots. The space (s) between dots (d) and dashes (D) within a Morse code of a letter (here digit of a number) has duration of 1 dot. The separation (S) between two letter codes has duration of 3 dots. (The duration between two words (numbers) is 7 dots.)

Only odd numbers >= 9 appear.

There are duration twins for pairs (n-1, n) with n ending with digits 10, 20, 30, 40 or 50, except for n = 10. The digits 1 and 9, 2 and 8, and 3 and 7 are pairs with identical duration (of 17, 15, and 13, respectively).

Links

Table of n, a(n) for n=0..76.

Wikipedia, Morse code

Formula

a(n) = S(n) + s(n) + dD(n), where S(n) = 3*(nrdigits(n) - 1), with nrdigits(n) the number of digits of n, s(n) = 4*nrdigits(n), and dD(n) = Sum_{j=1.. nrdigits(n)} 1*nrd(d_j) + 3*nrD(dj) = 1*A280913(n) + 3*A280916(n), with nrd(dj) the number of dots of the code of the j-th digits of n, and nrD(dj) the number of dashes of the code of the j-th digits of n.

Example

n = 10:  dsDsDsDsDSDsDsDsDsD, with a(10) = 3*(2-1) + 4*2 + ((1*1 + 3*4) + (1*0 + 3*5)) = 3 + 8 + (1*1 + 3*9)  = 39.

Mathematica

nd[n_] := 15 - 2 * If[n<5, n, 10-n]; a[n_] := Module[{d = IntegerDigits[n]}, 7 * Length[d] - 3 + Total[nd/@ d]]; Array[a, 100, 0] (* Amiram Eldar, Dec 04 2018 *)

Crossrefs

Cf. A060109, A280913, A280916.

Sequence in context: A215021 A215085 A241525 * A109410 A230339 A022975

Adjacent sequences: A321329 A321330 A321331 * A321333 A321334 A321335

Keyword

nonn,word,easy

Author

Wolfdieter Lang, Dec 03 2018

Status

approved