A380278 -id:A380278 - cp's OEIS frontend

A380495 Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by k distinct values and each subsequence enclosed by consecutive equal values is distinct.

1, 2, 1, 3, 1, 2, 4, 3, 2, 5, 6, 2, 3, 4, 2, 7, 3, 2, 5, 4, 2, 3, 8, 2, 6, 3, 2, 4, 5, 2, 3, 9, 2, 4, 3, 7, 5, 6, 3, 4, 10, 8, 3, 5, 4, 11, 3, 6, 7, 4, 3, 5, 9, 12, 3, 4, 6, 5, 3, 8, 4, 7, 3, 13, 5, 4, 3, 6, 10, 9, 3, 4, 5, 7, 3, 6, 4, 8, 3, 5, 14, 4, 3, 11, 6

Offset: 1

Neal Gersh Tolunsky, Jan 24 2025

nonn

Since the number of distinct terms in a subsequence is given by its enclosing values, the sequence remains the same whether we include those endpoints or not when checking the uniqueness of subsequences.
Without the condition that subsequences enclosed by consecutive equal values are distinct, this sequence would be A001511 (the ruler function).
Does each value occur finitely many times?

			a(7)=4: a(7) cannot be 1 because this would make a(5..7) a repeat of a(1..3) = 1,2,1. a(7) cannot be 2 or 3 as these would not enclose 2 or 3 distinct terms respectively. So a(7) must be 4.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Cf. A380278.

A380507 Lexicographically earliest infinite sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) terms and each subsequence enclosed by consecutive equal values is distinct.

Original entry on oeis.org

1, 2, 1, 3, 1, 3, 4, 3, 5, 3, 4, 6, 7, 8, 4, 6, 9, 7, 4, 6, 10, 11, 4, 6, 10, 12, 4, 6, 10, 13, 4, 6, 10, 14, 4, 6, 10, 13, 15, 6, 10, 16, 14, 6, 10, 13, 17, 6, 10, 18, 19, 6, 10, 13, 20, 6, 10, 18, 21, 6, 10, 13, 22, 6, 10, 18, 23, 6, 10, 13, 24, 6, 10, 18, 22

Offset: 1

Neal Gersh Tolunsky, Jan 25 2025

nonn

Endpoints are included when comparing subsequences enclosed by consecutive equal values.

			a(1) = 1 means that consecutive 1s enclose 1 term. For example: a(1..3) = [1,2,1] encloses [2].
a(2) = 2 means that consecutive 2s have length 2. In this case, there are no subsequences enclosed by a pair of 2s.
a(3) = 1 means that consecutive 3s enclose 1 term. For example, a(3..5) = [3,1,3] encloses [1].
a(7) = 4: a(7) cannot be 1 as this would repeat the subsequence [1,3,1], which was seen before at a(3..5). 2 and 3 would not enclose a(2) = 2 and a(3) = 1 terms respectively. So a(7) = 4, which has not occurred thus far.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Cf. A363654, A380278, A380495.

A380508 Lexicographically earliest sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) distinct terms and each subsequence enclosed by consecutive equal values is distinct.

Original entry on oeis.org

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

Offset: 1

Neal Gersh Tolunsky, Jan 26 2025

nonn

Endpoints are excluded when counting the number of distinct terms enclosed.

Endpoints are included when comparing subsequences enclosed.

			a(2) = 2, so 2's enclose 2 distinct terms. For example: a(2..6) = 2,1,3,1,2 enclosing the two distinct values in 1,3,1.
a(3) = 1, so 3's enclose 1 distinct term. In this case, there are no subsequences enclosed by a pair of 3s.
a(7) = 4: a(7) cannot be 1 as this would repeat the subsequence [1,2,1], which was seen before at a(1..3). 2 and 3 would not enclose a(2) = 2 and a(3) = 1 distinct terms respectively. So a(7) = 4, which has not occurred thus far.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Cf. A363654, A380278, A380495.

cp's OEIS Frontend

A380495 Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by k distinct values and each subsequence enclosed by consecutive equal values is distinct.

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A380507 Lexicographically earliest infinite sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) terms and each subsequence enclosed by consecutive equal values is distinct.

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A380508 Lexicographically earliest sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) distinct terms and each subsequence enclosed by consecutive equal values is distinct.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs