A097962 - OEIS

%I #11 Dec 09 2024 11:55:37

%S 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 83,85,87,89,210,301,410,501,610,701,810,901,2101,2103,2105,2107,2109,

%U 2121,2123,2125,2127,2129,2141,2143,2145,2147,2149,2161,2163,2165,2167,2169

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

%C 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 M. F. Hasler, <a href="/A097962/b097962.txt">Table of n, a(n) for n = 0..10000</a>

%t nn = 57; c[_] := False; a[0] = j = 0; p = 1; c[0] = True;

%t Do[k = j;

%t   While[(Set[q, Mod[#[[-1]], 2]];

%t     Nand[! c[k], Mod[#[[1]], 2] == p,

%t     Union[Length /@ SplitBy[#, EvenQ]] == {1}]) &[IntegerDigits[k]],

%t     k++]; Set[{a[n], j, p, c[k]}, {k, k, 1 - q, True}], {n, nn}];

%t Array[a, nn + 1, 0] (* _Michael De Vlieger_, Dec 09 2024 *)

%o (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 vector(50,i,t=if(i>1,nxt(t),0)) \\ _M. F. Hasler_, Mar 23 2019

%K nonn,base

%O 0,3

%A _Eric Angelini_, Sep 06 2004