[seqfan] Palindromic Subsequences Of Prime Differences
Leroy Quet
q1qq2qqq3qqqq at yahoo.com
Thu Mar 25 22:32:04 CET 2010
I am wondering if this sequence is in the EIS already. It doesn't look like it (searching using wildcards).
a(n) = the smallest prime p(k) (the kth prime) such that:
p(k+j)  p(k+j1) = p(n+k+1j)  p(n+kj),
for all j where 1 <= j <= n.
I get the sequence beginning:
(offset 1)
2, 3, 5, _, 7, _, 17
As an example: List the 8 primes starting with 17:
17,19,23,29,31,37,41,43
List the 7 differences between these consecutive primes:
2,4,6,2,6,4,2
Since this is a palindromic finite sequence, and since the sequence of 8 primes starting with 17 are the smallestvalued string of 8 primes having this property, then a(7) = 17.

First of all, I can't find a value for a(4) by checking all 97 differences between the primes in the "list" link of sequence A001223.
Is there even a prime where p(k+1)  p(k) = p(4+k)p(3+k), and p(k+2)  p(k+1) = p(3+k)p(2+k)?
Sorry that I am so dense, but this must be obvious.
And if a(4) exists, does a(n) exist for all n's?
And, oh yeah, can someone please extend the sequence?
Thanks,
Leroy Quet
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