A375559 L starts out as the list of positive integers; at the n-th iteration, a(n) is set to L(1); then L(1) is moved to its new position in L, in between the first two elements that it has never before been next to; repeat at the second step.

1, 2, 3, 1, 4, 2, 5, 3, 6, 1, 5, 7, 4, 6, 8, 2, 7, 9, 3, 8, 10, 1, 9, 11, 8, 5, 10, 12, 9, 4, 11, 13, 10, 2, 12, 6, 9, 14, 2, 11, 3, 13, 7, 10, 6, 11, 15, 3, 12, 14, 8, 13, 1, 12, 16, 13, 9, 15, 13, 5, 14, 1, 17, 10, 14, 16, 4, 15, 18, 16, 2, 15, 17, 19, 16, 11, 18, 7

Offset

1,2

Comments

Terms and correct definition by Ruud H.G. van Tol via SeqFan.

This sequence was called The Bad Neighbors sequence on the SeqFan list.

In the beginning, we insert L(1) between L(n+1) and L(n+2), but after a few steps, that doesn't work anymore because L(1) finds closer places between new neighbors.

Links

Table of n, a(n) for n=1..78.

Example

In a list of positive integers, no one wants to stay near their old neighbors. 1 doesn't want to stay near 2 anymore, so, it inserts itself between 3 and 4: 2, 3, 1, 4, 5, 6, 7, 8, ...
a(1) = 1
2 doesn't want to stay near 3 nor 1, so, it inserts itself between 4 and 5: 3, 1, 4, 2, 5, 6, 7, 8, ... .
a(2) = 2
3 doesn't want to stay near 2 nor 4 nor 1, so, it inserts itself between 5 and 6: 1, 4, 2, 5, 3, 6, 7, 8, ... .
a(3) = 3
Now, 1 doesn't want to stay near 2 nor 3 nor 4, so, it inserts itself between 7 and 8: 4, 2, 5, 3, 6, 7, 1, 8, ... .
a(4) = 1
And so on.

Crossrefs

Sequence in context: A118276 A023123 A023131 * A356625 A026276 A152201

Adjacent sequences: A375556 A375557 A375558 * A375560 A375561 A375562

Keyword

nonn

Author

Ali Sada, Aug 19 2024

Status

approved