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.

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

Offset: 1

Author

Eric Angelini and Carole Dubois, Feb 27 2022

Keywords

• base
• nonn

Comments

The sequence is a permutation of the positive integers.

Examples

			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)
		

Links

• Eric Angelini, A chain reaction producing primes, personal blog of the author, Feb. 2022.

Crossrefs

Cf. A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).