%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 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 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 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 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)
%Y The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.
%A _Michel Marcus_ and _N. J. A. Sloane_, Mar 10 2014