A358405 a(1) = 0; for n > 1, let a(n-1) = m; if a(n-1) is the first occurrence of m then a(n) = 0, but if there is a k < n-1 with a(k) = m, a(n) is the maximum of n-1-k and j, where a(j) is the first occurrence of m in the sequence.

0, 0, 1, 0, 2, 0, 2, 5, 0, 3, 0, 2, 5, 8, 0, 4, 0, 2, 6, 0, 3, 11, 0, 3, 10, 0, 3, 10, 25, 0, 4, 16, 0, 3, 10, 25, 29, 0, 5, 26, 0, 3, 10, 25, 29, 37, 0, 6, 29, 37, 46, 0, 5, 14, 0, 3, 14, 54, 0, 4, 29, 37, 46, 51, 0, 6, 19, 0, 3, 13, 0, 3, 10, 30, 0, 4, 16, 45, 0, 4, 16, 32, 0, 4, 16, 32, 82

Offset: 1

Author

Scott R. Shannon, Nov 14 2022

Keywords

• nonn
• look

Comments

This sequence uses the same selection rules as A358402 but here the maximum of the two offsets is chosen for a(n). The terms form an unusual pattern for larger values of n; see the linked images.

See A358406 for the index where each number first appears.

Examples

			a(5) = 2 as a(4) = 0 and a(2) = 0, these being separated by two terms.
a(8) = 5 as a(7) = 2 and 2 appears as the fifth term of the sequence. Note that the number of terms between the two previous occurrences of 2 is 7 - 5 = 2 which is smaller than 5, so 5 is chosen.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000.
• Scott R. Shannon, Image of the first 100000 terms.
• Scott R. Shannon, Image of the first 1000000 terms.
• Scott R. Shannon, Image of the first 10000000 terms.

Crossrefs

Cf. A358406, A181391, A358402, A358403, A171862, A171863.

Programs

Mathematica

nn = 120; q[] = c[] = 0; m = a[1] = 0; Do[If[c[#] == 0, k = 0; c[#] = q[#] = n - 1, k = Max[n - 1 - c[#], q[#]]; c[#] = n - 1] &[m]; a[n] = m = k; If[k == u, While[c[u] > 0, u++]], {n, 2, nn}]; Array[a, nn]

Python

from itertools import count, islice
def agen():
    an, first, prev = 0, {0: 1}, {0: 1}
    for n in count(2):
        yield an
        an1 = 0 if first[an] == n-1 else max(n-1-prev[an], first[an])
        if an1 not in first: first[an1] = prev[an1] = n
        prev[an] = n-1
        an = an1
print(list(islice(agen(), 87))) # Michael S. Branicky, Nov 14 2022