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A351997
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 odd numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
4
1, 2, 11, 3, 4, 13, 5, 6, 15, 7, 8, 17, 9, 10, 101, 103, 105, 107, 109, 111, 12, 19, 14, 21, 23, 25, 27, 29, 31, 16, 33, 18, 35, 20, 113, 22, 37, 24, 39, 26, 41, 43, 45, 47, 49, 51, 28, 53, 30, 115, 32, 55, 34, 57, 36, 59, 38, 61, 63, 65, 67, 69, 71, 40, 117, 42, 73, 44, 75, 46, 77, 48, 79, 50, 119, 52, 81
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 2 of a(2) = 2, turning this integer into 1, an odd number;
2 is expelled from a(2) = 2 and hits the leftmost 1 of a(3) = 11, "turning" this integer into 11, an odd number;
1 is expelled from a(3) = 11 and hits the 3 of a(4) = 3, turning this integer into 1, an odd number;
3 is expelled from a(4) = 3 and hits the 4 of a(5) = 4, turning this integer into 3, an odd number;
4 is expelled from a(5) = 4 and hits the 1 of a(6) = 13, turning this integer into 43, an odd number;
1 is expelled from a(6) = 13 and hits the 5 of a(7) = 5, turning this integer into 1, an odd number; etc.
CROSSREFS
Cf. A351996 (prime numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).
Sequence in context: A077805 A344539 A342043 * A104662 A333861 A338845
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Feb 27 2022
STATUS
approved