OFFSET

1,2

COMMENTS

Consider each index i as a location from which one can jump a(i) terms forwards or backwards. From all indices with the same a(n) value, every jump is to a distinct term.

Another way to define the sequence is to consider every possible ordered pair of values of the form (origin value, destination value)--every such ordered pair is distinct.

LINKS

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Pontus von Brömssen, Plot of (n,a(n)) for n = 1..1000000.

Pontus von Brömssen, Plot of (n, log(a(n))/log(n)) for n = 2..1000000.

EXAMPLE

a(5)=4 because:

a(5) cannot be 1 because then we would have two jumps from a term with the same value 2, both landing on the value 1--ordered pair (2,1) twice:

1, 2, 2, 3, 1

2---->1

1<----2

a(5) cannot be 2 because we would have two jumps from the same a(n) value 2 to the same value 2--ordered pair (2,2) twice:

1, 2, 2, 3, 2

2---->2

2<----2

a(5) cannot be 3 because we would have two jumps from the same a(n) value 2 to the same a(n) value 3--ordered pair (2,3) twice:

1, 2, 2, 3, 3

2---->3

2---->3

a(5) can be 4 without contradiction.

CROSSREFS

KEYWORD

nonn,look

AUTHOR

Neal Gersh Tolunsky, Jan 23 2024

EXTENSIONS

More terms from Pontus von Brömssen, Jan 24 2024

STATUS

approved