A281015 -id:A281015 - cp's OEIS frontend

A059852 Consider the English alphabet in Morse code (the International Morse radio telegraph code). Map a 'dit' to the digit one and a 'dah' to the digit 2, then express that ternary number in decimal.

5, 67, 70, 22, 1, 43, 25, 40, 4, 53, 23, 49, 8, 7, 26, 52, 77, 16, 13, 2, 14, 41, 17, 68, 71, 76

Offset: 1

Robert G. Wilson v, Feb 27 2001

Written in base 3, the terms read (12, 2111, 2121, 211, 1, 1121, 221, 1111, 11, 1222, 212, 1211, 22, 21, 222, 1221, 2212, 121, 111, 2, 112, 1112, 122, 2112, 2122, 2211). This contains all words over {1,2} with 1 to 4 letters except for 1122, 1212, 2221 and 2222, which correspond to the codes for Ü, Ä, Ö and CH. - M. F. Hasler, Jun 22 2020

			The sixth letter, F, is ".._." in Morse. This becomes 1121 in ternary and 43 in decimal, so a(6) = 43.

"Learning the Radiotelegraph Code," Seventh Edition, published by American Radio Relay League, West Hartford 7, Connecticut, 1955.
"Morse Code Course," Jeppesen and Company, Denver, Colorado, 1962.
"International Morse Code," prepared by Lt. Commander F.R.L. Tuthill, USNR and Lt. (J.G.) E.L. Battey, USNR, published by Insuline Corporation of America, Long Island City, NY.

Wikipedia, Morse code.

Cf. A060110, the same for numbers, and A060109, written in base 3.
Cf. A008777 (number of base 3 digits = dots and dashes in the n-th letter), A281015, A281017, A281018.
Cf. A105386, A105387 (ambiguous variants using digits 0 and 1).

A059852=digits(3008707498660932665486381130661318784490079420090,81) \\ or vecextract(apply(A032924,[1..28]), i) with i=numtoperm(26, 58849338891424664724588744) or i=vecsort(Vec("ETIANMSURWDKGOHVFuLaPJBXCYZQ"),,1)[1..26]. - M. F. Hasler, Jun 22 2020

Edited, links and crossrefs added by 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

A281020 Numbers with a prime number of raised dots in their Braille representation.

Original entry on oeis.org

0, 1, 4, 6, 8, 12, 13, 15, 19, 21, 31, 47, 51, 67, 70, 74, 76, 78, 87, 91, 100, 104, 106, 108, 111, 127, 137, 140, 144, 146, 148, 157, 160, 164, 166, 168, 172, 173, 175, 177, 179, 180, 184, 186, 188, 197, 202, 203, 205, 207, 209, 217, 220, 224, 226, 228, 230, 234, 236, 238

Offset: 1

Indranil Ghosh, Jan 13 2017

			67 is in the sequence. 67, as evident from the link uploaded above, has 11 raised dots ("o") in its Braille representation and 11 is prime.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Indranil Ghosh, Braille Numerals

Cf. A072283, A281015, A281017.

from sympy import isprime
B=[3, 1, 2, 2, 3, 2, 3, 4, 3, 2]
def a(n):
    s=0
    for i in str(n):
        s+=B[int(i)]
    return s+4
i=0
j=1
while j<=10000:
    if isprime(a(i))==True :
        print(f"{j} {i}")
        j+=1
    i+=1

cp's OEIS Frontend

A059852 Consider the English alphabet in Morse code (the International Morse radio telegraph code). Map a 'dit' to the digit one and a 'dah' to the digit 2, then express that ternary number in decimal.

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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.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python

A281020 Numbers with a prime number of raised dots in their Braille representation.

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Python