Starting the year 1999 I posted the
Puzzle 36, related to "Sequences of Descriptive terms".
In that very year,
and no later than 23/09/01,
Carlos Rivera, Mike Keith and Walter Schneider found in
total seven examples of sequences of descriptive all prime
example, all prime six terms self descriptive
1223, 112213, 21221113, 1211223113, 11122122132113. (CBRF,
Mike Keith contributed also with the estimations about how
many self-descriptive sequences one should have to examine
(of length N) in order to find one that is all primes. The
estimation made use of one Conway's
theorem, which says that self-descriptive
sequences grow (in terms of the number of digits)
proportional to 1.3^n.
On 29/1/99 the Keith's estimations predicted that "the
first length-7 chain will occur around 10^11, and the first
length-8 chain (which I can barely imagine ever finding!)
around 10^13. But, of course, we may be lucky and find one
On 25/09/01 Walter Schneider found the first seven
terms sequence in total accordance with the Keith's
"...One sequence of length
7 starting at 19.972.667.609 (found
today at 25.09.2001)..."
Perhaps is time now (almost twenty years later) to find the
one self-descriptive sequence of eight all prime
Q1. Send your smallest solution (self-descriptive
sequence of eight all prime terms.).
If we add the condition that the first term of the sequence
must be a palprime, the record is from Tiziano
sequence of five all prime terms:
111334101910341311 , 3123141110111911101314111321 ,
Q2. Send your smallest solution (self-descriptive sequence
of six all prime terms, the
first one, a palprime).
*Who passed away on the 11th April
in New Brunswick, New Jersey, at the age of 82