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

Author

Eric Angelini and Carole Dubois, Feb 03 2020

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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