Search: a331215 -id:a331215
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A331975
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Lexicographically earliest sequence of distinct positive integers such that three successive digits are always distinct.
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+10
3
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 30, 12, 31, 20, 13, 24, 15, 23, 14, 25, 16, 27, 18, 26, 17, 28, 19, 32, 40, 29, 34, 50, 35, 41, 36, 42, 37, 43, 51, 38, 45, 39, 46, 52, 47, 53, 48, 54, 60, 49, 56, 70, 57, 61, 58, 62, 59, 63, 71, 64, 72, 65, 73, 67, 80, 68, 74, 69, 75, 81, 76, 82, 78, 90, 79, 83, 91, 84
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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EXAMPLE
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As a(10) = 10, a(11) cannot start with a 1 or have a 0 in second position; thus a(11) = 21;
as a(11) = 21, a(12) cannot start with a 1 or a 2; thus a(12) = 30;
as a(12) = 30, a(13) = 12, smallest available integer not leading to an immediate contradiction;
as a(13) = 12, a(14) cannot start with 1 or 2; thus a(14) = 31, smallest available integer not leading to an immediate contradiction. Etc.
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PROG
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(Python)
from itertools import islice
def ok(s): return all(len(set(s[i:i+3]))==3 for i in range(len(s)-2))
def agen(): # generator of terms
aset, s, k, mink = {1}, "x1", 1, 2
while True:
yield k
k, avoid = mink, set(s)
while k in aset or not ok(s + str(k)): k += 1
aset.add(k)
s = (s + str(k))[-3:]
while mink in aset: mink += 1
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CROSSREFS
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Cf. A331215 (a variant with 4 successive distinct digits instead of 3).
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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A331989
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Lexicographically earliest sequence of distinct positive integers such that five successive digits are always distinct.
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+10
1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 41, 50, 24, 13, 52, 40, 15, 26, 30, 12, 43, 51, 20, 34, 16, 25, 31, 42, 53, 14, 27, 35, 18, 29, 36, 17, 28, 39, 45, 21, 37, 46, 19, 32, 47, 56, 38, 49, 57, 60, 48, 59, 61, 70, 54, 62, 71, 58, 63, 72, 80, 64, 73, 81, 65, 74, 82, 67, 90, 83, 69, 75, 84, 91, 68, 79, 102, 76, 85
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The 5 digits 1, 0, 2, 3, 4 of a(10), a(11) and the 1st digit of a(12) are distinct;
the 5 digits 0, 2, 3, 4, 1 of the 2nd digit of a(10), a(11) and a(12) are distinct;
the 5 digits 2, 3, 4, 1, 5 of a(11), a(12) and the 1st digit of a(13) are distinct;
the 5 digits 3, 4, 1, 5, 0 of the 2nd digit of a(11), a(12) and a(13) are distinct;
the 5 digits 4, 1, 5, 0, 2 of a(12), a(13) and the 1st digit of a(14) are distinct, etc.
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CROSSREFS
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Cf. A331975 (a variant with 3 successive distinct digits), A331215 (a variant with 4 successive distinct digits).
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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