A331975 -id:A331975 - cp's OEIS frontend

A331215 Lexicographically earliest sequence of distinct positive integers such that four successive digits are always distinct.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 14, 20, 13, 24, 15, 26, 17, 25, 16, 27, 18, 29, 30, 12, 34, 19, 28, 31, 40, 21, 35, 41, 32, 45, 36, 42, 37, 46, 38, 47, 39, 48, 50, 43, 51, 49, 52, 60, 53, 61, 54, 62, 57, 63, 58, 64, 59, 67, 80, 56, 70, 81, 65, 71, 68, 72, 69, 73, 82, 74, 83, 75, 84, 76, 85, 79, 86, 102

Offset: 1

Eric Angelini and Carole Dubois, Feb 03 2020

This is not A276766, though the first 63 terms are the same.

			The four digits of a(11) = 23 and a(12) = 14 are distinct;
the four digits of a(12) = 14 and a(13) = 20 are distinct;
but so are also the successive digits 3,1,4,2 visible in 23, 14, 20;
the four digits of a(13) = 20 and a(14) = 13 are distinct;
the four digits of a(14) = 13 and a(15) = 24 are distinct;
but so are also the successive digits 0,1,3,2 visible in 20,13,24; etc.

Carole Dubois, Table of n, a(n) for n = 1..5000

Cf. A331975 (a variant with 3 successive distinct digits instead of 4), A276766.

from itertools import islice
def ok(s): return all(len(set(s[i:i+4]))==4 for i in range(len(s)-3))
def agen(): # generator of terms
    aset, s, k, mink = {1}, "xy1", 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))[-4:]
        while mink in aset: mink += 1
print(list(islice(agen(), 79))) # Michael S. Branicky, Jun 30 2022

A331989 Lexicographically earliest sequence of distinct positive integers such that five successive digits are always distinct.

Original entry on oeis.org

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

Offset: 1

Eric Angelini and Carole Dubois, Feb 03 2020

			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.

Carole Dubois, Table of n, a(n) for n = 1..5000

Cf. A331975 (a variant with 3 successive distinct digits), A331215 (a variant with 4 successive distinct digits).

cp's OEIS Frontend

A331215 Lexicographically earliest sequence of distinct positive integers such that four successive digits are always distinct.

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