A239137 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e <= f, and S is always extended with the smallest integer not yet present in S.

1, 2, 10, 3, 12, 13, 14, 15, 4, 5, 16, 17, 6, 7, 18, 19, 8, 9, 20, 21, 30, 31, 32, 40, 41, 42, 43, 22, 102, 103, 23, 24, 25, 26, 27, 28, 29, 33, 104, 34, 35, 36, 37, 38, 39, 44, 105, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73

Offset: 1

Author

Michel Marcus, Mar 11 2014

Keywords

• nonn
• base

Comments

Computed by Lars Blomberg.

Numbers a(n) = 0, 1, 11 (mod 100) cannot be added to this sequence, otherwise the sequence would terminate with 1, 2, 10, 3, 11. - Gleb Ivanov, Dec 06 2021

References

• Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Links

• Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sg)
• Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

Crossrefs

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

Programs

Python

is_ok = lambda s: not any(s[i-2] <= s[i-1] <= s[i] for i in range(2, len(s)))
terms, appears, digits = [1], {1}, '1'
for i in range(100):
    t = 1
    while not(
        t not in appears
        and is_ok(digits + str(t))
        and t % 100 not in [0, 1, 11]
    ): t += 1
    terms.append(t); appears.add(t); digits = digits + str(t)
    digits = digits[-2:]
print(terms) # Gleb Ivanov, Dec 06 2021

Extensions

a(56) corrected by Gleb Ivanov, Dec 17 2021