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This is a variant of A244311, which (by definition) lacks single -digit terms and which uses the easily computed palindromic superpermutations produced by the classical recursive algorithm (see PARI code there), of non-minimal length A007489(n) for n > 5 and non-minimal lex order for n = 5. The lexico-first minimal-length superpermutations aren't palindromic, and therefore the corresponding primes aren't so here, in contrast to A244311.

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See A180632 for more about superpermutations, i.e., strings over a finite alphabet, say {1, ..., n}, that contain all permutations thereof as a substring. "Digits taken according to ..." means the number whose i-th digit is d[s[i]], 1 <= i <= A180632(#d), where d and s are the sequences of digits of the prime and of the superpermutation, respectively.

In March 2014, Ben Chaffin showed that minimal superpermutations of order n = 5 have length 153, and found all 8 distinct minimal superpermutations for of this case, kind (the lexicographically first being non-palindromic), so the 5-digit terms are known. For n = 6, Robin Houston has found thousands of a few months later several superpermutations of length 872, (one less than the previously conjectured minimal length), but we still don't know which is the shortest (and/or lexico-first) superpermutation for that case.

Robin Houston, <a href="http://arxiv.org/abs/1408.5108">Tackling the Minimal Superpermutation Problem</a>, arXiv:1408.5108 [math.CO], 2014.

In March 2014, Ben Chaffin showed that minimal See A180632 for more about superpermutations of order , i.e., strings over a finite alphabet, say {1, ..., n=5 have length 153, and he has found }, that contain all 8 distinct minimal superpermutations for this case, so permutations thereof as a substring. "Digits taken according to ..." means the 5number whose i-th digit terms is d[s[i]], 1 <= i <= A180632(#d), where d and s are known. For n=6, Houston has found thousands the sequences of superpermutations digits of length 872, but we still don't know which is the shortest (prime and/or lexico-first) the superpermutation for that case, respectively.

"Digits taken according to ..." means to take In March 2014, Ben Chaffin showed that minimal superpermutations of order n=5 have length 153, and found all 8 distinct minimal superpermutations for this case, so the number whose i5-th digit is d[s[i]], 1 <= i <= A180632(#d), where d and s terms are the sequences known. For n=6, Robin Houston has found thousands of digits superpermutations of length 872, but we still don't know which is the prime shortest (and the /or lexico-first) superpermutation, respectively for that case.

This is a variant of A244311, which (by definition) lacks single digit terms and which uses the easily computed palindromic superpermutations produced by the classical recursive algorithm (cf. see PARI code there) , of non-minimal length A007489(n) for n > 5 and non-minimal lex order for n = 5. The lexico-first minimal-length superpermutations aren't palindromic, and therefore the corresponding primes aren't so here, in contrast to A244311.

The superpermutations with minimal length of less than 5 objects are unique, (up to the choice of the symbols), the one for 3 objects is '"123121321'".

The prime p = 109 is in this sequence since under the above superpermutation (i.e., take taking the 1st, 2nd, 3rd, 1st, 2nd, 1st ... , 3rd, 2nd and 1st digit) it yields the number 109101901 which is also prime.

The minimal superpermutation of order 5 is the first one to be not palindromic, it reads "1234512...3254312". Correspondingly, when this "acts on" the 5-digit prime p = 11369, we get a non-palindromic 153 digit prime P = 1136911...3196311 whose 7th digit from the left is p's 2nd digit, '1', but whose 7th digit from the right is p's 3rd digit, '3'.

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In March 2014 , Ben Chaffin has shown showed that minimal superpermutations of order n=5 have length 153, and he has found all 8 distinct minimal superpermutations for this case, so the 5-digit terms are known. For n=6, Houston has found thousands of superpermutations of length 872, but we still don't know which is the shortest (and/or lexico-first) superpermutation for that case.

"Digits taken according to ..." means to take the number whose i-th digit is d[s[i]], 1 <= i <= A180632(#d), where d and s are the sequences of digits of the prime and the superpermutation, respectively.

This is a variant of A244311 , which (by definition) lacks single digit terms and which uses the easily computed palindromic superpermutations produced by the classical recursive algorithm (cf. PARI code there), of non-minimal length A007489(n) for n > 5 and non-minimal lex order for n = 5. The lexico-first minimal-length superpermutations aren't palindromic , and therefore the corresponding primes aren't here, in contrast to A244311.

proposed

editing