[seqfan] Re: Sequences taken from straight lines through the prime spiral.

Kevin Ryde user42_kevin at yahoo.com.au
Fri Jul 27 04:49:37 CEST 2018

David Sycamore <djsycamore at yahoo.co.uk> writes:
> central vertical (N~S) ... indices (A267682) seems to
> be there, (Rule 201 etc).  Its not clear (to me at least) what
> A267682 is all about and if it could have any connection with the
> prime spiral.

A267682 is another quadratic, if(n%2==0, n^2 - (n-2)/2, n^2 - (n-1)/2),
or pick your favourite (-1)^n etc for the cases.  Its rule 201 is full
rows except a fixed size alternating bit in the middle so cumulative odd
integers which is squares, less a bit.  As you noticed the even/odd
cases are interleaved A054556 and A033951 spiral spokes N,S.  I don't
suppose there'd be a connection to the spiral beyond triangle row
lengths vs spiral cycle length.

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