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

1,2

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

Table of n, a(n) for n=1..67.

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]

Prog

(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

Crossrefs

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

Sequence in context: A322000 A061196 A239136 * A252758 A249917 A176577

Adjacent sequences: A239134 A239135 A239136 * A239138 A239139 A239140

Keyword

nonn,base

Author

Michel Marcus, Mar 11 2014

Extensions

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

Status

approved