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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
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
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
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Mar 11 2014
EXTENSIONS
a(56) corrected by Gleb Ivanov, Dec 17 2021
STATUS
approved