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A349944 a (1) = 1; a(n) is the smallest number not yet present in the sequence such that the concatenation of a(n-1) and a(n) contains three consecutive descending digits d > e > f.

%I A349944 #15 Dec 30 2021 14:38:54
%S A349944 1,210,2,10,310,3,20,320,4,21,321,5,30,410,6,31,420,7,32,11,421,8,40,
%T A349944 430,9,41,431,12,100,432,13,101,510,14,102,103,104,105,42,15,43,16,50,
%U A349944 520,17,51,521,18,52,19,53,22,106,54,23,107,60,530,24,108,61
%N A349944 a (1) = 1; a(n) is the smallest number not yet present in the sequence such that the concatenation of a(n-1) and a(n) contains three consecutive descending digits d > e > f.
%C A349944 A permutation of the positive integers.
%e A349944 a(1) = 1;
%e A349944 a(2) = 210, because this is the smallest number not yet present in the sequence which, when concatenated with a(1) = 1 -> 1210, contains three consecutive digits 2 > 1 > 0;
%e A349944 a(3) = 2, because this is the smallest number not yet present in the sequence which, when concatenated with a(2) = 210 -> 2102, contains three consecutive digits 2 > 1 > 0;
%e A349944 a(4) = 10, because this is the smallest number not yet present in the sequence which, when concatenated with a(3) = 2 -> 210, contains three consecutive digits 2 > 1 > 0.
%o A349944 (Python)
%o A349944 is_ok = lambda s: any(s[i-2] > s[i-1] > s[i] for i in range(2, len(s)))
%o A349944 terms, appears = [1], {1}
%o A349944 for i in range(100):
%o A349944     t = 1
%o A349944     while t in appears or not is_ok(str(terms[-1]) + str(t)):
%o A349944         t += 1
%o A349944     terms.append(t); appears.add(t)
%o A349944 print(terms)
%Y A349944 Cf. A239083, A239137.
%K A349944 nonn,base
%O A349944 1,2
%A A349944 _Gleb Ivanov_, Dec 06 2021