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A309540 a(n) is the smallest positive number not yet in the sequence that contains exactly one even digit and exactly one odd digit from a(n-1), and no digit in a(n) is repeated.

%I A309540 #34 Jan 12 2025 09:06:32
%S A309540 10,102,12,21,120,103,30,130,104,14,41,124,123,23,32,132,125,25,52,
%T A309540 152,126,16,61,106,105,50,150,107,70,170,108,18,81,128,127,27,72,172,
%U A309540 129,29,92,192,142,134,34,43,143,140,109,90,190,160,136,36,63,163
%N A309540 a(n) is the smallest positive number not yet in the sequence that contains exactly one even digit and exactly one odd digit from a(n-1), and no digit in a(n) is repeated.
%H A309540 Robert Israel, <a href="/A309540/b309540.txt">Table of n, a(n) for n = 1..40534</a>
%e A309540 a(2)=102: a(2) is not 100 (since zero would be repeated), nor 101 (since 1 would be repeated).
%p A309540 filter:= proc(n) local L;
%p A309540   L:= convert(n,base,10);
%p A309540   nops(L) = nops(convert(L,set)) and convert(L mod 2,set) = {0,1};
%p A309540 end proc:
%p A309540 Cands:= select(filter, [$11 .. 1000]): nC:= nops(Cands):
%p A309540 R:= 10: r:= 10: r0, r1:= selectremove(type, convert(convert(r,base,10),set),even):
%p A309540 for count from 1 do
%p A309540   found:= false;
%p A309540   for i from 1 to nC+1-count do
%p A309540     x:= Cands[i];
%p A309540     Lx:= convert(convert(x,base,10),set);
%p A309540     if nops(Lx intersect r0) = 1 and nops(Lx intersect r1) = 1 then
%p A309540       found:= true;
%p A309540       R:= R, x;
%p A309540       r:= x;
%p A309540       Cands:= subsop(i=NULL, Cands);
%p A309540       r0, r1:= selectremove(type, convert(convert(r,base,10),set),even);
%p A309540       break
%p A309540     fi
%p A309540   od;
%p A309540   if not found then break fi;
%p A309540 od:
%p A309540 R; # _Robert Israel_, Jan 09 2025
%Y A309540 Cf. A184992, A318700, A309390, A309539, A076654.
%K A309540 nonn,base,fini,full,look
%O A309540 1,1
%A A309540 _Enrique Navarrete_, Aug 06 2019
%E A309540 Edited by _Robert Israel_, Jan 10 2025