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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.
4
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
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini ansd Carole Dubois, Feb 27 2022
STATUS
approved