A366122 Pick any term t: exactly two of the t terms following t are distinct and larger than t.

2, 3, 4, 2, 5, 3, 6, 2, 4, 7, 2, 3, 8, 2, 4, 3, 9, 2, 5, 3, 10, 2, 4, 6, 2, 11, 3, 2, 4, 7, 12, 2, 3, 4, 2, 5, 13, 2, 3, 4, 6, 2, 14, 3, 2, 4, 7, 2, 3, 15, 2, 4, 3, 8, 2, 5, 16, 2, 3, 4, 6, 9, 2, 3, 17, 2, 4, 3, 2, 5, 10, 2, 18, 3, 2, 4, 5, 2, 3, 6, 11, 19, 2, 3, 4, 2, 5, 3, 6, 2, 20, 3, 2, 4, 7, 2, 3, 5, 2, 4, 21

Offset

1,1

Comments

Starting with a(1) = 2, this is the lexicographically earliest sequence with this property.

a(n) >= 2 as we need exactly two of the t terms following t to be distinct and larger than t.

If we admit that the two terms are equal, see A366121.

Is this sequence a fractal one?

Links

Table of n, a(n) for n=1..101.

Example

Two distinct terms out of 2 following a(1) = 2 are > 2: they are 3 and 4.
Two distinct terms out of 3 following a(2) = 3 are > 3: they are 4 and 5.
Two distinct terms out of 4 following a(3) = 4 are > 4: they are 5 and 6.
Two distinct terms out of 2 following a(4) = 2 are > 2: they are 5 and 3.
Two distinct terms out of 5 following a(5) = 5 are > 5: they are 6 and 7.
Two distinct terms out of 3 following a(6) = 3 are > 3: they are 6 and 4.
Two distinct terms out of 6 following a(7) = 6 are > 6: they are 7 and 8.
Two distinct terms out of 2 following a(8) = 2 are > 2: they are 4 and 7; etc.

Crossrefs

Cf. A366121.

Sequence in context: A305893 A374477 A325980 * A182718 A212645 A364951

Adjacent sequences: A366119 A366120 A366121 * A366123 A366124 A366125

Keyword

nonn

Author

Eric Angelini, Sep 30 2023

Extensions

More terms from Giorgos Kalogeropoulos, Oct 03 2023

Status

approved