cp's OEIS Frontend

A351997 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 odd numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.

%I A351997 #7 Mar 13 2022 19:24:57
%S A351997 1,2,11,3,4,13,5,6,15,7,8,17,9,10,101,103,105,107,109,111,12,19,14,21,
%T A351997 23,25,27,29,31,16,33,18,35,20,113,22,37,24,39,26,41,43,45,47,49,51,
%U A351997 28,53,30,115,32,55,34,57,36,59,38,61,63,65,67,69,71,40,117,42,73,44,75,46,77,48,79,50,119,52,81
%N A351997 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 odd numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
%C A351997 The sequence is a permutation of the integers > 0.
%H A351997 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 A351997 1 is expelled from a(1) = 1 and hits the 2 of a(2) = 2, turning this integer into 1, an odd number;
%e A351997 2 is expelled from a(2) = 2 and hits the leftmost 1 of a(3) = 11, "turning" this integer into 11, an odd number;
%e A351997 1 is expelled from a(3) = 11 and hits the 3 of a(4) = 3, turning this integer into 1, an odd number;
%e A351997 3 is expelled from a(4) = 3 and hits the 4 of a(5) = 4, turning this integer into 3, an odd number;
%e A351997 4 is expelled from a(5) = 4 and hits the 1 of a(6) = 13, turning this integer into 43, an odd number;
%e A351997 1 is expelled from a(6) = 13 and hits the 5 of a(7) = 5, turning this integer into 1, an odd number; etc.
%Y A351997 Cf. A351996 (prime numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).
%K A351997 base,nonn
%O A351997 1,2
%A A351997 _Eric Angelini_ and _Carole Dubois_, Feb 27 2022