[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 k-th prime) such that:
p(k+j) - p(k+j-1) = p(n+k+1-j) - p(n+k-j),
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 smallest-valued 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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