old seqs related to dodecahedron, help needed

N. J. A. Sloane njas at research.att.com
Sat Oct 6 22:23:53 CEST 2007

njas reasonably commented on A131741:

"Definition is not clear. There are several ways that it could be
clarified but I do not know which was intended. - njas, Oct 06 2007"

My intention was as follows, but I would be interested in knowing how
accidently obscure I was by seeing serious alternative interpretations
of the title. In retrospect, the word "picked" was confusing.  Also,
starting with 2 different a(0) and a(1) would in general yield a
different sequence. I shall not submit viable alternatives as new
sequences, out of concern for "less" interest and more obscurity.

"Smallest prime such that n numbers may be picked with no three terms
in arithmetic progression."

Start with a(1) = prime(1) = 2, a(2) = prime(2) = 3.

a(n) is the smallest prime p > a(n-1) such that no subset of
cardinality 3 or more of {a(1), a(2), ... a(n)} form an arithmetic
progression. (I thought that the condition p > a(n-1) was redundant).
(I thought that excluding arithmetic progressions of length 3
guaranteed that there could be none longer than 3).

Or, I thought equivalently:

Start with a(1) = prime(1) = 2, a(2) = prime(2) = 3.

For n>2, a(n) is the smallest (positive, real, in A000040) prime p such that,
for all i < j <n,  there does not exist an integer k such that k =
a(n) - a(j) = a(j) - a(i).

Please do not blame Ray Chandler for any obscurity that I created.

Once this is resolved, I intend to submit what Ray Chandler extended
and programmed, namely the semiprime equivalent.

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