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%I #41 Jun 10 2022 09:01:30
%S 1,2,10,3,11,4,12,13,14,15,5,6,16,17,7,8,18,19,9,20,21,22,23,24,25,26,
%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,200,201,121,122,130,202
%N 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 More than the usual number of terms are given in order to show that the pattern breaks after 120.
%C Computed by Lars Blomberg.
%C This is the first (Sa) of a family of 25 similar sequences. For others see
%C A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.
%C The sequence So (see link) has d > e = f in the definition. It does not have its own entry in the OEIS because it begins with the numbers 1 through 99. Using x-y to indicate the numbers from x through y, the sequence So begins like this:
%C 1-99,101-109,120,110-112,121,201,113,122-130,114,131,202,132-140,115,141,
%C 203,142-150,116,151,204,152-160,117,161,205,162-170,118,171,206, 172-180,
%C 119,181,207,182-191, 208,192-199,209, 210,212-219,230, 220-223,231, 224,232,
%C 301, 225,233-240,226,241,227,242, ...
%C Likewise, the sequence Sw is omitted for a similar reason. It has d = e > f in the definition, and begins 1-89,99,999,9999,99999,999999,9999999,..., continuing with strings of 9's.
%C Again, the sequences Sx and Sy are omitted because they are too close to A130571.
%C Sx (which has d = e >= f) begins
%C 1-11,20,12-19,21,22,30,23-29,31-33,40,34-39,41-44,50,45-49,51-55,60,56-59,
%C 61-66, 70,67-69,71-77,80,78,79,81-88,90,89,100,91-98,101,120,102-109,
%C 112-119,121,122,300, 123-133,400,134-144,500,145-155,600,156-166,700,
%C 167-177,800,178-188,900,189-198,200-202, ...
%C and Sy (d = e = f) begins
%C 1-11,20,12-19,21,22,30,23-29,31-33,40,34-39,41-44,50,45-49,51-55,60,56-59,
%C 61-66, 70,67-69,71-77,80,78,79,81-88,90,89,91-110,112-221,223-332,334-443,
%C 445-554,556-665, 667-776,778-887,889-899,1001,900-989,1002,990-998,1003-1010,...
%C The sequences Sd, Si, Sl, Sq are omitted because they do not have enough terms to warrant their own entries.
%D Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013
%H Gleb Ivanov, <a href="/A239083/b239083.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/LittleEqualGreat.htm">Less than <, Equal to =, Greater than ></a> (see sequence Sa)
%H Eric Angelini, <a href="/A239083/a239083.pdf">Less than <, Equal to =, Greater than ></a> [Cached copy, with permission of the author] (see sequence Sa)
%t a[1]=1;a[n_]:=a[n]=Block[{k=1},While[MemberQ[s=Array[a,n-1],k]||Or@@(#<#2<#3&@@@Partition[Flatten[IntegerDigits/@Join[s[[-2;;]],{k}]],3,1]),k++];k];Array[a,126] (* _Giorgos Kalogeropoulos_, May 13 2022 *)
%o (Python)
%o is_ok = lambda s: not any(s[i-2] < s[i-1] < s[i] for i in range(2, len(s)))
%o terms, appears, digits = [1],{1},'1'
%o for i in range(100):
%o t = 1
%o while not(t not in appears and is_ok(digits + str(t))):
%o t += 1
%o terms.append(t); appears.add(t); digits = digits + str(t)
%o digits = digits[-2:]
%o print(terms) # _Gleb Ivanov_, Dec 04 2021
%Y The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.
%K nonn,base,look
%O 1,2
%A _Michel Marcus_ and _N. J. A. Sloane_, Mar 10 2014
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