cp's OEIS Frontend

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.

%I A358405 #25 Jan 21 2023 20:28:01
%S A358405 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,
%T A358405 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,
%U A358405 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
%N 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.
%C A358405 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.
%C A358405 See A358406 for the index where each number first appears.
%H A358405 Scott R. Shannon, <a href="/A358405/b358405.txt">Table of n, a(n) for n = 1..10000</a>.
%H A358405 Scott R. Shannon, <a href="/A358405/a358405.png">Image of the first 100000 terms</a>.
%H A358405 Scott R. Shannon, <a href="/A358405/a358405_1.png">Image of the first 1000000 terms</a>.
%H A358405 Scott R. Shannon, <a href="/A358405/a358405_2.png">Image of the first 10000000 terms</a>.
%e A358405 a(5) = 2 as a(4) = 0 and a(2) = 0, these being separated by two terms.
%e A358405 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.
%t A358405 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]
%o A358405 (Python)
%o A358405 from itertools import count, islice
%o A358405 def agen():
%o A358405     an, first, prev = 0, {0: 1}, {0: 1}
%o A358405     for n in count(2):
%o A358405         yield an
%o A358405         an1 = 0 if first[an] == n-1 else max(n-1-prev[an], first[an])
%o A358405         if an1 not in first: first[an1] = prev[an1] = n
%o A358405         prev[an] = n-1
%o A358405         an = an1
%o A358405 print(list(islice(agen(), 87))) # _Michael S. Branicky_, Nov 14 2022
%Y A358405 Cf. A358406, A181391, A358402, A358403, A171862, A171863.
%K A358405 nonn,look
%O A358405 1,5
%A A358405 _Scott R. Shannon_, Nov 14 2022