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.

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

Table of n, a(n) for n=1..77.

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

Adjacent sequences: A351994 A351995 A351996 * A351998 A351999 A352000

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 27 2022

Status

approved