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%I #14 Mar 13 2022 19:24:43
%S 1,10,101,103,107,109,111,11,12,2,3,4,13,14,17,15,5,6,21,7,8,19,16,27,
%T 9,18,23,29,33,20,113,30,117,31,22,39,24,37,25,43,41,47,51,49,53,59,
%U 63,57,69,61,67,71,32,73,34,77,35,79,36,81,83,89,93,26,87,99,28,121,38,123,40,119,42,127,44,91,50
%N A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only prime numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
%C The sequence is a permutation of the positive integers.
%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2022/02/a-chain-reaction-producing-primes.html">A chain reaction producing primes</a>, personal blog of the author, Feb. 2022.
%e 1 is expelled from a(1) = 1 and hits the 0 of a(2) = 10, turning this integer into 11, a prime;
%e 0 is expelled from a(2) = 10 and hits the 0 of a(3) = 101, leaving this prime unchanged;
%e 0 is expelled from a(3) = 101 and hits the 0 of a(4) = 103, leaving this prime unchanged;
%e 0 is expelled from a(4) = 103 and hits the 0 of a(5) = 107, leaving this prime unchanged;
%e 0 is expelled from a(5) = 107 and hits the 0 of a(6) = 109, leaving this prime unchanged;
%e 0 is expelled from a(6) = 109 and hits the middle 1 of a(7) = 111, turning this integer into 101, a prime;
%e 1 is expelled from a(7) = 111 and hits one 1 of a(8) = 11, leaving this prime unchanged;
%e 1 is expelled from a(8) = 11 and hits the 2 of a(9) = 12, turning this integer into 11, a prime;
%e 2 is expelled from a(9) = 12 and hits the 2 of a(10) = 2, leaving this prime unchanged; etc.
%e From _Jon E. Schoenfield_, Mar 01 2022: (Start)
%e The chain reaction is depicted in the chart below:
%e .
%e | Step | Step | Step | Step | Step | Step | Step | Step | Step | Step |
%e | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
%e | | | | | | | | | | |
%e | : | | | | | | | | | |
%e | 1 | | | | | | | | | |
%e | 10 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 |
%e | | 0 | | | | | | | | |
%e | 101 | 101 | 101 | 101 | 101 | 101 | 101 | 101 | 101 | 101 |
%e | | | 0 | | | | | | | |
%e | 103 | 103 | 103 | 103 | 103 | 103 | 103 | 103 | 103 | 103 |
%e | | | | 0 | | | | | | |
%e | 107 | 107 | 107 | 107 | 107 | 107 | 107 | 107 | 107 | 107 |
%e | | | | | 0 | | | | | |
%e | 109 | 109 | 109 | 109 | 109 | 109 | 109 | 109 | 109 | 109 |
%e | | | | | | 0 | | | | |
%e | 111 | 111 | 111 | 111 | 111 | 111 | 101 | 101 | 101 | 101 |
%e | | | | | | | 1 | | | |
%e | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 |
%e | | | | | | | | 1 | | |
%e | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 11 | 11 |
%e | | | | | | | | | 2 | |
%e | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
%e (End)
%Y Cf. A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Feb 27 2022
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