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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.

%I A239137 #23 Dec 17 2021 02:16:38
%S A239137 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,
%T A239137 43,22,102,103,23,24,25,26,27,28,29,33,104,34,35,36,37,38,39,44,105,
%U A239137 45,46,47,48,49,50,51,52,53,54,60,61,62,63,64,65,70,71,72,73
%N 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.
%C A239137 Computed by Lars Blomberg.
%C A239137 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
%D A239137 Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013
%H A239137 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/LittleEqualGreat.htm">Less than <, Equal to =, Greater than ></a> (see sequence Sg)
%H A239137 Eric Angelini, <a href="/A239083/a239083.pdf">Less than <, Equal to =, Greater than ></a> [Cached copy, with permission of the author]
%o A239137 (Python)
%o A239137 is_ok = lambda s: not any(s[i-2] <= s[i-1] <= s[i] for i in range(2, len(s)))
%o A239137 terms, appears, digits = [1], {1}, '1'
%o A239137 for i in range(100):
%o A239137     t = 1
%o A239137     while not(
%o A239137         t not in appears
%o A239137         and is_ok(digits + str(t))
%o A239137         and t % 100 not in [0, 1, 11]
%o A239137     ): t += 1
%o A239137     terms.append(t); appears.add(t); digits = digits + str(t)
%o A239137     digits = digits[-2:]
%o A239137 print(terms) # _Gleb Ivanov_, Dec 06 2021
%Y A239137 The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.
%K A239137 nonn,base
%O A239137 1,2
%A A239137 _Michel Marcus_, Mar 11 2014
%E A239137 a(56) corrected by _Gleb Ivanov_, Dec 17 2021