Need help with an arbitrary sequence

[Aitzaz Imtiaz]

Hello!

I am making a sequence, and I would appreciate a lot of help. Please note that I am an undergraduate student in BS CS doing my first semester, and I am a non-native in both formal mathematical language and English.

With no further ado, I'd like informed opinions here on the following sequence and someone to determine if this is worth some general interest or artificial enough to be here.

1. Take a number spiral and circle all the primes. All circled here are primes, (single circled one's are not the part of this sequence)

2. Moving rules on this ladder: You can move diagonal, up, down, left or right. 

3. In this spiral path the condition for a prime number to be accepted is if it moves in a prime path towards 1 that is, lets say we count the cost of moving from prime to 1 where the direction count is prime.

i.e. 2-->1 (reject since 1 is not prime), 19--->5--->1 (accepted because it cost 2 nodes to move, 2 is prime).

I would appreciate insights, questions, and further observations, and if possible a program to implement the sequence. And the most basic of all, is the idea generally interesting or acceptable for OEIS?

The sequence is: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 83, 89, 97, 101, 103, 107, 109, 113, 179, 181...

Regards,

Aitzaz.

P.S. I know artificial means something forced and not occurring naturally, if this is artificial, I will be happy to move on, but as a request, it would be kind enough for someone to explain what makes it artificial.

[D. S. McNeil]

I read this as something like "Primes at prime Chebyshev distance from the center of the Ulam spiral", or expanded, "Primes P such that max(|x|, |y|) is prime, where (x, y) is the position of P in the Ulam spiral with 1 at the origin."

And since we can compute that Chebyshev distance via a formula from any number, this is "primes p where ceil((sqrt(p)-1)/2) is also prime".

In that interpretation, though, wouldn't 173 be a sequence member too?

  Distance 2: [11, 13, 17, 19, 23]
  Distance 3: [29, 31, 37, 41, 43, 47]
  Distance 5: [83, 89, 97, 101, 103, 107, 109, 113]
  Distance 7: [173, 179, 181, 191, 193, 197, 199, 211, 223]

I get this:

Doug

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[Aitzaz Imtiaz]

Doug

Thank you so much for this. This sequence is not on OEIS and yes. I used Google Gemini to confirm this. Its interesting enough to add on OEIS

Regards.

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