A331975 Lexicographically earliest sequence of distinct positive integers such that three successive digits are always distinct.

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

Offset: 1

Author

Eric Angelini and Carole Dubois, Feb 03 2020

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A331215 (a variant with 4 successive distinct digits instead of 3).

Programs

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
print(list(islice(agen(), 79))) # Michael S. Branicky, Jun 30 2022