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

1,2

Links

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A341935 A256079 A216556 * A068860 A158699 A247107

Adjacent sequences: A331972 A331973 A331974 * A331976 A331977 A331978

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 03 2020

Status

approved