Yes, Allan, and yes. And we backtrack to extend the seq. Until we reach the bridge you mention. Best, É.
Le 20 mai 2020 à 01:53, Allan Wechsler <acwacw@gmail.com> a écrit :
If I understand correctly, the internal digits -- the digits that are not first and not last -- do not matter at all, and we merely choose them to achieve distinctness and lexicographic priority, right?
If we reach a point where there are no primes between Q and Q+99, do we stop and declare victory, or do we backtrack in hopes of finding a longer solution?
Regardless, it appears that Q cannot leap over a prime gap of 100 or more. This first happens between the consecutive primes 370261 and 370373; the gap is 112. So here at least is an upper limit.
On Tue, May 19, 2020 at 7:03 PM Éric Angelini <eric.angelini@skynet.be> wrote:
And yes — we want S to be the lexicographically earliest seq of distinct positive terms with this property. É.
Le 20 mai 2020 à 00:46, Éric Angelini <eric.angelini@skynet.be> a écrit :
Hello Math-Fun, This seq S is finite — but how many terms in it? And which is the last one? S = 1, 3, 4, 2, 41, 42, 21, 43, 44, 22, 45, etc. We are only interested in the cumulative sum Q which must be prime at every stage. The first term of Q is 13 — and this prime comes from the digits squeezing the 1st comma; the 2nd term of Q is 13 + 34 = 47 (prime) and 34 comes from the digits squeezing the 2nd comma; the 3rd term of Q is 47 + 42 = 89 (prime) and 42 comes from the digits squeezing the 3rd comma; the 4th term of Q is 89 + 24 = 113 (prime) and 24 comes from the digits squeezing the 4th comma; the 5th term of Q is 113 + 14 = 127 (prime) and 14 comes from the digits squeezing the 5th comma; etc. We don’t accept terms of S ending in 0 (zero). Best, É.
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