A351999 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.

1, 2, 3, 4, 30, 610, 611, 5, 6, 110, 7, 307, 612, 8, 9, 80, 613, 10, 614, 31, 13, 20, 615, 15, 21, 22, 11, 23, 12, 41, 32, 51, 25, 61, 210, 71, 317, 24, 33, 14, 26, 310, 16, 410, 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

Offset: 1

Author

Eric Angelini and Carole Dubois, Feb 27 2022

Keywords

• base
• nonn

Comments

The sequence is a permutation of the integers > 0.

Examples

			1 is expelled from a(1) = 1 and hits the 2 of a(2) = 2, "turning" this integer into 2, a Fibonacci number;
2 is expelled from a(2) = 2 and hits the 3 of a(3) = 3, "turning" this integer into 3, a Fibonacci number;
3 is expelled from a(3) = 3 and hits the 4 of a(4) = 4, turning this integer into 3, a Fibonacci number;
4 is expelled from a(4) = 4 and hits the 0 of a(5) = 30, turning this integer into 34, a Fibonacci number;
0 is expelled from a(5) = 30 and hits the 0 of a(6) = 610, "turning" this integer into 610, a Fibonacci number;
0 is expelled from a(6) = 610 and hits the rightmost 1 of a(7) = 611, turning this integer into 610, a Fibonacci number;
1 is expelled from a(7) = 611 and hits the 5 of a(8) = 5, turning this integer into 1, a Fibonacci number;
5 is expelled from a(8) = 5 and hits the 6 of a(9) = 6, turning this integer into 5, a Fibonacci number;
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.
		

Links

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

Crossrefs

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