A379381 a(1)=1, a(2)=2; thereafter, a(n) is the smallest positive integer such that for any value k, the number of distinct values between a pair of k's is distinct, counting k itself.

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

Offset: 1

Author

Neal Gersh Tolunsky, Dec 21 2024

Keywords

• nonn

Comments

Note that we are considering every pair of equal values, not just those that appear consecutively.

Examples

			a(7)=4: We cannot have a(7)=1 here because this would make a(1..7) = 1, 2, 1, 2, 3, 3, 1 enclose the same number of terms as a(3..7) = 1, 2, 3, 3, 1 (3 distinct values). We cannot have a(7)=2 because this would mean a(4..7) = 2, 3, 3, 2 encloses 2 values, which we had at a(2..4) = 2, 1, 2. a(7) cannot be 3 because this would repeat a(5-6) = 3, 3 with a(6-7) = 3, 3, again enclosing 1 distinct value. So a(7) = 4 without restriction.
		

Links

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

Crossrefs

Cf. A330896, A366691, A370577, A281511.