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A097962 Slowest increasing sequence where the digits, taken one by one, show the pattern even/odd/even/odd/even...

%I A097962 #11 Dec 09 2024 11:55:37
%S A097962 0,1,2,3,4,5,6,7,8,9,21,23,25,27,29,41,43,45,47,49,61,63,65,67,69,81,
%T A097962 83,85,87,89,210,301,410,501,610,701,810,901,2101,2103,2105,2107,2109,
%U A097962 2121,2123,2125,2127,2129,2141,2143,2145,2147,2149,2161,2163,2165,2167,2169
%N A097962 Slowest increasing sequence where the digits, taken one by one, show the pattern even/odd/even/odd/even...
%C A097962 Distinct from A098951, which is not required to be increasing. The first 31 terms are identical, but here a(30) = 210 must be followed by a(31) = 301, while there 210 is followed by 10. - _M. F. Hasler_, Mar 23 2019
%H A097962 M. F. Hasler, <a href="/A097962/b097962.txt">Table of n, a(n) for n = 0..10000</a>
%t A097962 nn = 57; c[_] := False; a[0] = j = 0; p = 1; c[0] = True;
%t A097962 Do[k = j;
%t A097962   While[(Set[q, Mod[#[[-1]], 2]];
%t A097962     Nand[! c[k], Mod[#[[1]], 2] == p,
%t A097962     Union[Length /@ SplitBy[#, EvenQ]] == {1}]) &[IntegerDigits[k]],
%t A097962     k++]; Set[{a[n], j, p, c[k]}, {k, k, 1 - q, True}], {n, nn}];
%t A097962 Array[a, nn + 1, 0] (* _Michael De Vlieger_, Dec 09 2024 *)
%o A097962 (PARI) nxt(n,d=digits(n))={if(!bittest(#d,0), forstep(i=#d,1,-1, 10>(d[i]+=2)&& return(fromdigits(d)); d[i]-=10);  d||return(1); d[#d]=if(d[1]%=2,10,21); fromdigits(Vecrev(d)), 10>d[1]+=1, d[1]=d[1]*10+d[#d]; fromdigits(d)\10, d[1]=21; fromdigits(d))}
%o A097962 vector(50,i,t=if(i>1,nxt(t),0)) \\ _M. F. Hasler_, Mar 23 2019
%K A097962 nonn,base
%O A097962 0,3
%A A097962 _Eric Angelini_, Sep 06 2004