%I
%S 1,2,3,4,5,6,7,8,9,210,101,212,103,214,105,216,107,218,109,230,121,
%T 232,123,234,125,236,127,238,129,250,141,252,143,254,145,256,147,258,
%U 149,270,161,272,163,274,165,276,167,278,169,290,181,292,183
%N Terms as well as digits are of alternating parity; this is the lexicographically earliest injective sequence with this property.
%C The sum of two successive terms is odd and the sum of two successive digits is odd, too. The sequence could be started with an additional 0 and then be extended always with the smallest integer not yet present in the sequence and not leading to a contradiction.  _Eric Angelini_ and _JeanMarc Falcoz_, Jan 31 2017
%H Carole Dubois, <a href="/A217555/b217555.txt">Table of n, a(n) for n = 1..5673</a>
%H Eric Angelini, <a href="http://list.seqfan.eu/pipermail/seqfan/2012October/010252.html">Odd/even: integers and digits alternate</a>, SeqFan mailing list, Oct 06 2012
%F Conjectures from _Colin Barker_, Jan 16 2020: (Start)
%F G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + 201*x^9  110*x^10 + 110*x^11  110*x^12 + 110*x^13  110*x^14 + 110*x^15  110*x^16 + 110*x^17  110*x^18  80*x^19) / ((1  x)^2*(1 + x)*(1  x + x^2  x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = a(n1) + a(n10)  a(n11) for n>20.
%F (End)
%o (PARI) {a(n,show=1,a=1,u)=for( i=2, n, u+=1<<a; show & print1(a","); for(t=1,9e9, bittest(u,t) & next; bittest(t+a,0)  next; !bittest(a%10 + t\10^(#Str(t)1),0) & (t+=10^(#Str(t)1)1) & next; my(tt=t); while( tt>9, bittest( tt+0+tt\=10, 0 )  next(2)); a=t; break )); a}
%Y Sequence A217556 is a simplified variant.
%Y See also A217559, A217560, where "parity" is replaced by "primality".
%K nonn,base,changed
%O 1,2
%A _Eric Angelini_ and _M. F. Hasler_, Oct 06 2012
