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Lexicographically first sequence of nonprime terms (with no duplicates) that turns into a sequence of prime terms (with no duplicates) by applying the "comma-permutation" simultaneously at every comma. [The "comma-permutation" is explained in the Comments section.]
2

%I #40 Apr 26 2020 07:40:25

%S 1,21,12,32,33,91,14,72,111,15,92,321,301,102,322,721,901,702,931,312,

%T 332,942,152,153,74,75,34,93,703,711,121,731,132,762,361,932,972,171,

%U 741,951,154,704,104,912,981,161,362,781,371,372,992,3002,3012,1011,782,1022,7021,993,112,3031,994,323

%N Lexicographically first sequence of nonprime terms (with no duplicates) that turns into a sequence of prime terms (with no duplicates) by applying the "comma-permutation" simultaneously at every comma. [The "comma-permutation" is explained in the Comments section.]

%C The "comma-permutation" swaps the last digit of a(n) and the first digit of a(n+1) for every n. For instance [2016,2017] becomes [2012,6017] and [2016,2017,2018] turns into [2012,6012,7018].

%C The sequence is always extended with the smallest integer not yet present that does not lead to a contradiction.

%C No term ends in "0" as this "0" would start a term of the prime sequence.

%H Rémy Sigrist, <a href="/A228092/b228092.txt">Table of n, a(n) for n = 1..10000</a> (first 205 terms from Eric Angelini and Jean-Marc Falcoz)

%H Rémy Sigrist, <a href="/A228092/a228092.gp.txt">PARI program for A228092</a>

%e Under the "comma-permutation" the nine nonprime terms [1,21,12,32,33,91,14,72,111,15] become the primes [2,11,13,23,29,31,17,41,211].

%o (PARI) See Links section.

%Y Cf. A274408.

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jun 17 2016