Search: a358405 -id:a358405
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A358406
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The index of A358405 where n first appears, or 0 if n never appears.
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+20
3
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1, 3, 5, 10, 16, 8, 19, 141, 14, 190, 25, 22, 416, 70, 54, 162, 32, 308, 169, 67, 93, 203, 118, 513, 196, 29, 40, 200, 861, 37, 74, 1081, 82, 216, 208, 363, 90, 46, 375, 1675, 1091, 333, 1407, 812, 166, 78, 51, 1099, 115, 193, 1243, 64, 595, 98, 58, 367, 617, 235, 325, 766, 2137, 272, 124
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OFFSET
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0,2
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COMMENTS
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LINKS
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PROG
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(Python)
from itertools import count, islice
def agen():
k, an, first, prev = 0, 0, {0: 1}, {0: 1}
for n in count(2):
while k in first: yield first[k]; k += 1
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A358402
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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 minimum of n-1-k and j, where a(j) is the first occurrence of m in the sequence.
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+10
4
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0, 0, 1, 0, 1, 2, 0, 1, 3, 0, 1, 3, 3, 1, 3, 2, 6, 0, 1, 3, 5, 0, 1, 3, 4, 0, 1, 3, 4, 4, 1, 3, 4, 3, 2, 6, 17, 0, 1, 3, 6, 5, 21, 0, 1, 3, 6, 6, 1, 3, 4, 18, 0, 1, 3, 5, 14, 0, 1, 3, 5, 5, 1, 3, 4, 14, 9, 0, 1, 3, 6, 17, 35, 0, 1, 3, 6, 6, 1, 3, 4, 16, 0, 1, 3, 5, 21, 43, 0, 1, 3, 6, 14, 27, 0, 1
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OFFSET
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1,6
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COMMENTS
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This sequence can be considered a variation of Van Eck's sequence, see A181391, but where the sequence forms a loop of numbers, joined at its first and last term before each a(n) is calculated. When a previously unseen number first appears the following term is 0, and as 0 appears as the first term of the sequence, the next term after these 0's will always be 1.
See A358403 for the index where each number first appears.
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LINKS
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EXAMPLE
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a(5) = 1 as a(4) = 0 and 0 appears as the first term of the sequence.
a(6) = 2 as a(5) = 1 and a(3) = 1, these being separated by two terms.
a(17) = 6 as a(16) = 2 and 2 appears as the sixth term of the sequence. Note that the number of terms between the two previous occurrences of 2 is 16 - 6 = 10 which is larger than 6, so 6 is chosen.
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MATHEMATICA
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nn = 120; q[_] = c[_] = 0; m = a[1] = 0; Do[If[c[#] == 0, k = 0; c[#] = q[#] = n - 1, k = Min[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] (* Michael De Vlieger, Jan 21 2023 *)
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PROG
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(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 min(n-1-prev[an], first[an])
if an1 not in first: first[an1] = prev[an1] = n
prev[an] = n-1
an = an1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A358403
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The index of A358402 where n first appears, or 0 if n never appears.
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+10
3
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1, 3, 6, 9, 25, 21, 17, 109, 198, 67, 860, 114, 148, 261, 57, 137, 82, 37, 52, 215, 447, 43, 105, 404, 267, 163, 414, 94, 154, 1292, 184, 716, 142, 669, 243, 73, 1685, 126, 360, 209, 329, 324, 355, 88, 542, 300, 887, 366, 422, 492, 1053, 1754, 256, 941, 946, 711, 679, 178, 283, 3273, 2221, 225
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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LINKS
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PROG
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(Python)
from itertools import count, islice
def agen():
k, an, first, prev = 0, 0, {0: 1}, {0: 1}
for n in count(2):
while k in first: yield first[k]; k += 1
an1 = 0 if first[an] == n-1 else min(n-1-prev[an], first[an])
if an1 not in first: first[an1] = prev[an1] = n
prev[an] = n-1
an = an1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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