

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.


4



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
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OFFSET

1,2


COMMENTS

The sequence is a permutation of the integers > 0.


LINKS

Table of n, a(n) for n=1..74.
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, 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.


CROSSREFS

Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A000290 (the squares).
Sequence in context: A201050 A299321 A248537 * A330073 A266584 A104773
Adjacent sequences: A351997 A351998 A351999 * A352001 A352002 A352003


KEYWORD

base,nonn


AUTHOR

Eric Angelini and Carole Dubois, Feb 27 2022


STATUS

approved



