A280998 -id:A280998 - cp's OEIS frontend

A281015 Numbers with a prime number of dots in their International Morse numeral representation.

2, 3, 5, 7, 8, 11, 12, 14, 16, 18, 19, 20, 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, 80, 81, 83, 85, 87, 89, 91, 92, 94, 96, 98, 99, 101, 102, 104, 106, 108, 109, 110, 111, 113, 115, 117, 119, 120, 122, 124, 126

Offset: 1

Indranil Ghosh, Jan 13 2017

The Morse code is written in current ITU standard.

Indices of primes in A280913. - M. F. Hasler, Jun 22 2020

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

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

Cf. A060109 (Morse code for n), A280913 (number of dots in Morse code for n).
Cf. A281017 (same for dashes), A281018 (intersection of the two).
Cf. A280998, A280999.

select( {is_A281015(n)=isprime(A280913(n))}, [0..150]) \\ M. F. Hasler, Jun 22 2020

# uses[A280913]
from sympy import isprime
i=0
j=1
while j<=100:
    if isprime(A280913(i)):
        print(str(j)+" "+str(i))
        j+=1
    i+=1

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

A280999 Numbers with a prime number of 0's in their binary reflected Gray code representation.

Original entry on oeis.org

7, 8, 12, 14, 15, 16, 17, 19, 23, 24, 25, 27, 28, 29, 30, 33, 34, 35, 36, 38, 39, 40, 44, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 61, 63, 64, 66, 68, 69, 70, 72, 73, 75, 76, 77, 78, 80, 81, 83, 87, 88, 89, 91, 92, 93, 94, 96, 98, 100, 101, 102, 104, 105, 107

Offset: 1

Indranil Ghosh, Jan 12 2017

			27 is in the sequence because the binary reflected Gray Code representation of 27 is 10110 which has 2 0's and 2 is prime.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Wikipedia, Gray code.

Cf. A014550, A144754, A280998.

Select[Range[100], PrimeQ[DigitCount[BitXor[#, Floor[#/2]], 2, 0]] &] (* Amiram Eldar, May 01 2021 *)

is(n)=isprime(logint(n,2)-hammingweight(bitxor(n, n>>1))+1) \\ Charles R Greathouse IV, Jan 13 2017

A281014 Numbers with both prime number of 0's and prime number of 1's in their binary reflected Gray code representation.

Original entry on oeis.org

8, 12, 14, 16, 17, 19, 23, 24, 25, 27, 28, 29, 30, 33, 35, 39, 47, 49, 51, 55, 57, 59, 61, 64, 69, 73, 75, 77, 81, 83, 87, 89, 91, 93, 96, 101, 105, 107, 109, 112, 117, 120, 124, 126, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147

Offset: 1

Indranil Ghosh, Jan 13 2017

This sequence is the intersection of A280998 and A280999.

			27 is in the sequence as it is present in both the sequences A280998 and A280999.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Wikipedia, Gray code.

Cf. A014550, A280998, A280999.

Select[Range[150], And @@ PrimeQ[DigitCount[BitXor[#, Floor[#/2]], 2]] &] (* Amiram Eldar, May 01 2021 *)

is(n)=isprime(logint(n,2)-hammingweight(bitxor(n, n>>1))+1) && isprime(hammingweight(bitxor(n, n>>1))) \\ Charles R Greathouse IV, Jan 13 2017

cp's OEIS Frontend

A281015 Numbers with a prime number of dots in their International Morse numeral representation.

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

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A280999 Numbers with a prime number of 0's in their binary reflected Gray code representation.

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A281014 Numbers with both prime number of 0's and prime number of 1's in their binary reflected Gray code representation.

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Author

Keywords

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Examples

Links

Crossrefs

Programs

Mathematica

PARI