A351998 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 even numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.

1, 10, 12, 14, 16, 18, 20, 2, 3, 22, 4, 5, 24, 6, 7, 26, 8, 9, 28, 11, 30, 32, 34, 36, 38, 40, 13, 42, 15, 44, 17, 46, 19, 48, 21, 50, 52, 54, 56, 58, 60, 23, 62, 25, 64, 27, 66, 29, 68, 31, 70, 72, 74, 76, 78, 80, 33, 82, 35, 84, 37, 86, 39, 88, 41, 90, 92, 94, 96, 98, 100, 43, 102, 45, 104, 47, 106, 49

Offset

1,2

Comments

The sequence is a permutation of the integers > 0.

Links

Table of n, a(n) for n=1..78.

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 1 of a(2) = 10, "turning" this integer into 10, an even number;
1 is expelled from a(2) = 10 and hits the 1 of a(3) = 12, "turning" this integer into 12, an even number;
1 is expelled from a(3) = 12 and hits the 1 of a(4) = 14, "turning" this integer into 14, an even number;
1 is expelled from a(4) = 14 and hits the 1 of a(5) = 16, "turning" this integer into 16, an even number;
1 is expelled from a(5) = 16 and hits the 1 of a(6) = 18, "turning" this integer into 18, an even number;
1 is expelled from a(6) = 18 and hits the 2 of a(7) = 20, turning this integer into 10, an even number;
2 is expelled from a(7) = 20 and hits the 2 of a(8) = 2, "turning" this integer into 2, an even number;
2 is expelled from a(8) = 2 and hits the 3 of a(9) = 3, turning this integer into 2, an even number;
3 is expelled from a(9) = 3 and hits the leftmost 2 of a(10) = 22, turning this integer into 32, an even number; etc.

Crossrefs

Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).

Sequence in context: A337028 A050769 A330724 * A088381 A163750 A356660

Adjacent sequences: A351995 A351996 A351997 * A351999 A352000 A352001

Keyword

base,nonn

Author

Eric Angelini ansd Carole Dubois, Feb 27 2022

Status

approved