A370577 Lexicographically earliest sequence such that for any value m, the number of distinct values between a pair of consecutive m's is distinct.

1, 1, 2, 1, 2, 2, 3, 1, 2, 3, 3, 4, 1, 2, 3, 4, 3, 4, 4, 5, 1, 2, 3, 4, 5, 5, 6, 1, 2, 3, 4, 5, 6, 4, 5, 6, 5, 6, 6, 7, 1, 2, 3, 4, 5, 6, 7, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 5, 6, 7, 8, 7, 8, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 8, 9, 9, 10, 1, 2, 3, 4, 5, 6, 7

Offset: 1

Author

Neal Gersh Tolunsky, Feb 22 2024

Keywords

• nonn

Examples

			The first terms with the number of distinct values enclosed by m = 1..4 below:
   n|  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
...
a(n)|  1  1  2  1  2  2  3  1  2  3  3  4  1  2  3  4  3  4  4  5  1  2  3
...
----+---------------------------------------------------------------------
 1's|     0,    1,          2,             3,                      4,
...
 2's|              1, 0,       2,             3,                      4,
...
 3's|                             2, 0,          3,    1,                4,
...
 4's|                                               3,    1, 0,
...
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf.A330896, A366691, A281511.

Programs

Python

from itertools import islice
def agen(): # generator of terms
    e, a = set(), []
    while True:
        an, allnew = 0, False
        while not allnew:
            allnew, an, nd = True, an+1, None
            for i in range(len(a)-1, -1, -1):
                if an == a[i]:
                    nd = len(set(a[i+1:]))
                    if (an, nd) in e: allnew = False
                    break
        yield an; a.append(an); e.add((an, nd))
print(list(islice(agen(), 86))) # Michael S. Branicky, Feb 22 2024

Extensions

More terms from Michael S. Branicky, Feb 22 2024