A280916 -id:A280916 - cp's OEIS frontend

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

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

A281017 Numbers with a prime number of dashes in their International Morse numeral representation.

Original entry on oeis.org

0, 2, 3, 7, 8, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 35, 36, 38, 41, 43, 44, 46, 47, 49, 50, 52, 53, 57, 58, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 76, 78, 81, 83, 85, 87, 89, 92, 94, 96, 98, 101, 103, 107, 109, 110, 112, 118, 121, 125, 129, 130, 134, 136, 143

Offset: 1

Indranil Ghosh, Jan 13 2017

The Morse code is written in current ITU standard.

Indices of primes in A280916. - M. F. Hasler, Jun 22 2020

			27 is in the sequence because 27 in its Morse numeral representation is written as '..--- --...' which has 5 dashes and 5 is prime.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Wikipedia, Morse Code

Cf. A060109 (Morse code for n), A280916 (number of dashes in Morse code for n).
Cf. A281015 (same for dots), A281018 (intersection of the two).
Cf. A280998, A280999.

select( {is_A281017(n)=isprime(A280916(n))}, [0..150]) \\ M. F. Hasler, Jun 22 2020

# uses[A280916]
from sympy import isprime
i=0
j=1
while j<=100:
    if isprime(A280916(i)):
        print(str(j)+" "+str(i))
        j+=1
    i+=1

This A281017 = { n | A280916(n) is prime }. - M. F. Hasler, Jun 22 2020

A281018 Numbers with a prime number of dots and a prime number of dashes in their International Morse numeral representation.

Original entry on oeis.org

2, 3, 7, 8, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 47, 49, 50, 52, 58, 61, 63, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 92, 94, 96, 98, 101, 109, 110, 190, 200, 355, 445, 454, 456, 465, 535, 544, 546, 553, 557, 564, 566, 575, 645

Offset: 1

Indranil Ghosh, Jan 13 2017

This uses the current ITU standard Morse code.

This sequence is the intersection of A281015 and A281017.

			27 is in the sequence because it is both in A281015 and A281017.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Wikipedia, Morse Code

Cf. A280913, A280916, A281015, A281017.

Cf. A060109 (Morse code for n).

select( {is_A281018(n)=is_A281017(n)&&is_A281015(n)}, [0..666]) \\ M. F. Hasler, Jun 22 2020

# uses[A280913, A280916]
from sympy import isprime
i=0
j=1
while j<=1000:
    if isprime(A280913(i)) and isprime(A280916(i)):
        print(str(j)+" "+str(i))
        j+=1
    i+=1

A321332 Duration of Morse code representation of n.

Original entry on oeis.org

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

Wolfdieter Lang, Dec 03 2018

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).

			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.

Wikipedia, Morse code

Cf. A060109, A280913, A280916.

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 *)

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.

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

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A281017 Numbers with a prime number of dashes in their International Morse numeral representation.

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A281018 Numbers with a prime number of dots and a prime number of dashes in their International Morse numeral representation.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python

A321332 Duration of Morse code representation of n.

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Author

Keywords

Comments

Examples

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Programs

Mathematica

Formula