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

1,2

Comments

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

Links

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

Example

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.

Prog

(Python)
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

Crossrefs

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

Sequence in context: A114806 A239664 A276766 * A039229 A054659 A331989

Adjacent sequences: A331212 A331213 A331214 * A331216 A331217 A331218

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 03 2020

Status

approved