A352000 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 square numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
1, 2, 15, 3, 16, 4, 5, 20, 100, 101, 6, 10, 102, 25, 35, 26, 45, 7, 129, 8, 11, 9, 40, 103, 36, 46, 19, 56, 21, 66, 12, 55, 22, 65, 13, 76, 184, 80, 104, 29, 75, 229, 85, 31, 86, 41, 39, 96, 42, 95, 43, 124, 81, 82, 111, 83, 161, 84, 49, 59, 23, 224, 121, 125, 87, 284, 131, 261, 141, 60, 105, 24, 61, 88
Offset: 1
Examples
1 is expelled from a(1) = 1 and hits the 2 of a(2) = 2, turning this integer into 1, a square number; 2 is expelled from a(2) = 2 and hits the 1 of a(3) = 15, turning this integer into 25, a square number; 1 is expelled from a(3) = 15 and hits the 3 of a(4) = 3, turning this integer into 1, a square number; 3 is expelled from a(4) = 3 and hits the 1 of a(5) = 16, turning this integer into 36, a square number; 1 is expelled from a(5) = 16 and hits the 4 of a(6) = 4, turning this integer into 1, a square number; 4 is expelled from a(6) = 4 and hits the 5 of a(7) = 5, turning this integer into 4, a square number; 5 is expelled from a(7) = 5 and hits the 0 of a(8) = 20, turning this integer into 25, a square number; 0 is expelled from a(8) = 20 and hits a 0 of a(9) = 100, "turning" this integer into 100, a square number; 0 is expelled from a(9) = 100 and hits the rightmost 1 of a(10) = 101, turning this integer into 100, a square number; etc.
Links
- Eric Angelini, A chain reaction producing primes, personal blog of the author, Feb. 2022.
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