Can a Sequence Visit 0, 1, and 5 Infinitely Often?

  • Thread starter adrivit
  • Start date
  • Tags
    Sequence
In summary, the conversation discusses the construction of a sequence that visits the numbers 0, 1, and 5 infinitely often. The initial sequence proposed, with a3n=0, a3n+1=1, and a3n+2=5 for all n, is found to not visit the numbers infinitely many times. There is a suggestion for a different sequence that visits all natural numbers infinitely, but the conversation also considers using modular arithmetic or the field R^inf with the subfield N.
  • #1
adrivit
6
0
Construct a sequence that visits the numbers 0,1,5 infinitely often.
A sequence Sn visits a number A when for infinitely many n in N, Sn = A. Example: The sequence (-1)^n visits -1 and 1 infinitely.
 
Physics news on Phys.org
  • #2
What's wrong with a3n= 0, a3n+1= 1, a3n+2= 5 for all n?
 
  • #3
But, the function doesn't visit 0,1,5 infinitely many times here does it?
 
  • #4
I'm sorry, I misunderstood. Thanks for the solution!
 
  • #5
How about the sequence which visits all N infinitely?
 
  • #6
Do you have any ideas? There is one that is fairly similar to the one that visits 0,1 and 5 infinitely often
 
  • #7
I was wondering whether N mod N would do the trick. Or maybe considering the field R^inf and the sub field N inside that. But I am not sure of either.
 

FAQ: Can a Sequence Visit 0, 1, and 5 Infinitely Often?

What is the significance of the sequence of 0,1,5 in ANT?

The sequence of 0,1,5 in ANT refers to the order in which certain genes are activated during embryonic development. This sequence is crucial for the proper formation and development of the body plan in many animals, including insects and crustaceans. It is also known as the "ANT sequence" because it was first discovered in the fruit fly species Drosophila melanogaster, which has the gene ANT responsible for this sequence.

How does the sequence of 0,1,5 contribute to the formation of body segments?

The sequence of 0,1,5 is responsible for the formation of segments in the body of organisms. This is achieved through the activation of specific genes in a specific order, which leads to the development of distinct body segments with unique characteristics. The first number, 0, marks the beginning of the sequence and is responsible for the formation of the head segment. The second number, 1, is responsible for the formation of the first thoracic segment, and the third number, 5, is responsible for the formation of the first abdominal segment.

Are there any other sequences similar to 0,1,5 in other organisms?

Yes, there are other sequences similar to 0,1,5 in other organisms. This type of sequence, known as "gap gene" sequences, has been found in various animals, including vertebrates like mice and zebrafish. While the specific numbers may vary, the overall pattern of gene activation and body segment formation is similar.

Can the sequence of 0,1,5 be altered or mutated?

Yes, the sequence of 0,1,5 can be altered or mutated. This can lead to developmental abnormalities and defects in body segment formation. In some cases, these mutations can be lethal, while in others, they may lead to visible changes in the body plan of an organism.

How does the sequence of 0,1,5 relate to evolutionary development?

The sequence of 0,1,5 is conserved across many animal species, suggesting that it is an important mechanism for proper body segment formation. This indicates that this sequence has been evolutionarily conserved and may have played a crucial role in the development and diversification of body plans in animals over time.

Back
Top