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A370577
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Lexicographically earliest sequence such that for any value m, the number of distinct values between a pair of consecutive m's is distinct.
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1
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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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,
...
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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