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%I #7 Mar 13 2022 19:25:26
%S 1,2,15,3,16,4,5,20,100,101,6,10,102,25,35,26,45,7,129,8,11,9,40,103,
%T 36,46,19,56,21,66,12,55,22,65,13,76,184,80,104,29,75,229,85,31,86,41,
%U 39,96,42,95,43,124,81,82,111,83,161,84,49,59,23,224,121,125,87,284,131,261,141,60,105,24,61,88
%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 square 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 integers > 0.
%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 2 of a(2) = 2, turning this integer into 1, a square number;
%e 2 is expelled from a(2) = 2 and hits the 1 of a(3) = 15, turning this integer into 25, a square number;
%e 1 is expelled from a(3) = 15 and hits the 3 of a(4) = 3, turning this integer into 1, a square number;
%e 3 is expelled from a(4) = 3 and hits the 1 of a(5) = 16, turning this integer into 36, a square number;
%e 1 is expelled from a(5) = 16 and hits the 4 of a(6) = 4, turning this integer into 1, a square number;
%e 4 is expelled from a(6) = 4 and hits the 5 of a(7) = 5, turning this integer into 4, a square number;
%e 5 is expelled from a(7) = 5 and hits the 0 of a(8) = 20, turning this integer into 25, a square number;
%e 0 is expelled from a(8) = 20 and hits a 0 of a(9) = 100, "turning" this integer into 100, a square number;
%e 0 is expelled from a(9) = 100 and hits the rightmost 1 of a(10) = 101, turning this integer into 100, a square number; etc.
%Y Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A000290 (the squares).
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Feb 27 2022
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