%I
%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 A239083A239086, A239136A239139, A239087A239090, A239215A239218, 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 xy to indicate the numbers from x through y, the sequence So begins like this:
%C 199,101109,120,110112,121,201,113,122130,114,131,202,132140,115,141,
%C 203,142150,116,151,204,152160,117,161,205,162170,118,171,206, 172180,
%C 119,181,207,182191, 208,192199,209, 210,212219,230, 220223,231, 224,232,
%C 301, 225,233240,226,241,227,242, ...
%C Likewise, the sequence Sw is omitted for a similar reason. It has d = e > f in the definition, and begins 189,99,999,9999,99999,999999,9999999,..., 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 111,20,1219,21,22,30,2329,3133,40,3439,4144,50,4549,5155,60,5659,
%C 6166, 70,6769,7177,80,78,79,8188,90,89,100,9198,101,120,102109,
%C 112119,121,122,300, 123133,400,134144,500,145155,600,156166,700,
%C 167177,800,178188,900,189198,200202, ...
%C and Sy (d = e = f) begins
%C 111,20,1219,21,22,30,2329,3133,40,3439,4144,50,4549,5155,60,5659,
%C 6166, 70,6769,7177,80,78,79,8188,90,89,91110,112221,223332,334443,
%C 445554,556665, 667776,778887,889899,1001,900989,1002,990998,10031010,...
%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 A239083A239086, A239136A239139, A239087A239090, A239215A239218, A239235.
%K nonn,base
%O 1,2
%A _Michel Marcus_ and _N. J. A. Sloane_, Mar 10 2014
