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