

A351996


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.


4



1, 10, 101, 103, 107, 109, 111, 11, 12, 2, 3, 4, 13, 14, 17, 15, 5, 6, 21, 7, 8, 19, 16, 27, 9, 18, 23, 29, 33, 20, 113, 30, 117, 31, 22, 39, 24, 37, 25, 43, 41, 47, 51, 49, 53, 59, 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
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OFFSET

1,2


COMMENTS

The sequence is a permutation of the positive integers.


LINKS

Table of n, a(n) for n=1..77.
Eric Angelini, A chain reaction producing primes, personal blog of the author, Feb. 2022.


EXAMPLE

1 is expelled from a(1) = 1 and hits the 0 of a(2) = 10, turning this integer into 11, a prime;
0 is expelled from a(2) = 10 and hits the 0 of a(3) = 101, leaving this prime unchanged;
0 is expelled from a(3) = 101 and hits the 0 of a(4) = 103, leaving this prime unchanged;
0 is expelled from a(4) = 103 and hits the 0 of a(5) = 107, leaving this prime unchanged;
0 is expelled from a(5) = 107 and hits the 0 of a(6) = 109, leaving this prime unchanged;
0 is expelled from a(6) = 109 and hits the middle 1 of a(7) = 111, turning this integer into 101, a prime;
1 is expelled from a(7) = 111 and hits one 1 of a(8) = 11, leaving this prime unchanged;
1 is expelled from a(8) = 11 and hits the 2 of a(9) = 12, turning this integer into 11, a prime;
2 is expelled from a(9) = 12 and hits the 2 of a(10) = 2, leaving this prime unchanged; etc.
From Jon E. Schoenfield, Mar 01 2022: (Start)
The chain reaction is depicted in the chart below:
.
 Step  Step  Step  Step  Step  Step  Step  Step  Step  Step 
 1  2  3  4  5  6  7  8  9  10 
          
 :          
 1          
 10  11  11  11  11  11  11  11  11  11 
  0         
 101  101  101  101  101  101  101  101  101  101 
   0        
 103  103  103  103  103  103  103  103  103  103 
    0       
 107  107  107  107  107  107  107  107  107  107 
     0      
 109  109  109  109  109  109  109  109  109  109 
      0     
 111  111  111  111  111  111  101  101  101  101 
       1    
 11  11  11  11  11  11  11  11  11  11 
        1   
 12  12  12  12  12  12  12  12  11  11 
         2  
 2  2  2  2  2  2  2  2  2  2 
(End)


CROSSREFS

Cf. A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).
Sequence in context: A231889 A066327 A277442 * A077712 A219763 A214390
Adjacent sequences: A351993 A351994 A351995 * A351997 A351998 A351999


KEYWORD

base,nonn


AUTHOR

Eric Angelini and Carole Dubois, Feb 27 2022


STATUS

approved



