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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 Fibonacci numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
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%I #9 Mar 13 2022 19:25:18

%S 1,2,3,4,30,610,611,5,6,110,7,307,612,8,9,80,613,10,614,31,13,20,615,

%T 15,21,22,11,23,12,41,32,51,25,61,210,71,317,24,33,14,26,310,16,410,

%U 34,35,45,36,510,50,616,710,327,81,19,27,337,17,347,37,357,52,91,82,133,28,29,233,333,18,39,44

%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 Fibonacci 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 2, a Fibonacci number;

%e 2 is expelled from a(2) = 2 and hits the 3 of a(3) = 3, "turning" this integer into 3, a Fibonacci number;

%e 3 is expelled from a(3) = 3 and hits the 4 of a(4) = 4, turning this integer into 3, a Fibonacci number;

%e 4 is expelled from a(4) = 4 and hits the 0 of a(5) = 30, turning this integer into 34, a Fibonacci number;

%e 0 is expelled from a(5) = 30 and hits the 0 of a(6) = 610, "turning" this integer into 610, a Fibonacci number;

%e 0 is expelled from a(6) = 610 and hits the rightmost 1 of a(7) = 611, turning this integer into 610, a Fibonacci number;

%e 1 is expelled from a(7) = 611 and hits the 5 of a(8) = 5, turning this integer into 1, a Fibonacci number;

%e 5 is expelled from a(8) = 5 and hits the 6 of a(9) = 6, turning this integer into 5, a Fibonacci number;

%e 6 is expelled from a(9) = 110 and hits the leftmost 1 of a(7) = 110, turning this integer into 610, a Fibonacci number; etc.

%Y Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351998 (even numbers left), A352000 (square numbers left), A000045 (Fibonacci numbers).

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, Feb 27 2022