A318698 - OEIS

%I #23 Feb 05 2020 16:54:45

%S 0,101,10,1,12,11,14,13,16,15,18,17,70,7,72,21,2,23,20,25,22,27,24,29,

%T 26,61,6,63,30,3,32,31,34,33,36,35,38,37,74,41,4,43,40,45,42,47,44,49,

%U 46,65,50,5,52,51,54,53,56,55,58,57,76,67,60,69,62,121,28,81,8

%N a(n) is the smallest nonnegative integer of the same parity as n, not yet in the sequence, that shares a digit with a(n-1); a(0)=0.

%C Conjecture: This is a permutation of the nonnegative integers.

%C The one-digit integers appear in the following order: 0,1,7,2,6,3,4,5,8,9.

%H Robert Israel, <a href="/A318698/b318698.txt">Table of n, a(n) for n = 0..10000</a>

%e a(1)=101 since 101 is the smallest odd nonnegative integer not yet in the sequence that shares the digit 0 with a(0)=0;

%e a(2)=10 since 10 is the smallest even nonnegative integer not yet in the sequence that shares the digit 0 (and 1) with a(1)=101.

%p N:= 1000: # to stop before the first term > N

%p S0:= [seq(i,i=2..N,2)]: S1:= [seq(i,i=1..N,2)]:

%p D0:= map(t -> convert(convert(t,base,10),set), S0):

%p D1:= map(t -> convert(convert(t,base,10),set), S1):

%p A[0]:= 0: Da:= {0}: found:= true:

%p for n from 1 while found do

%p   found:= false;

%p   if n::even then

%p     for j from 1 to nops(D0) do

%p       if Da intersect D0[j] <> {} then

%p         found:= true;

%p         A[n]:= S0[j];

%p         Da:= D0[j];

%p         S0:= subsop(j=NULL, S0);

%p         D0:= subsop(j=NULL, D0);

%p         break

%p       fi

%p     od

%p   else

%p     for j from 1 to nops(D1) do

%p       if Da intersect D1[j] <> {} then

%p         found:= true;

%p         A[n]:= S1[j];

%p         Da:= D1[j];

%p         S1:= subsop(j=NULL, S1);

%p         D1:= subsop(j=NULL, D1);

%p         break

%p       fi

%p     od

%p   fi

%p od:

%p seq(A[i],i=0..n-2); # _Robert Israel_, Feb 05 2020

%Y Cf. A107353, A297352, A297353.

%K nonn,base

%O 0,2

%A _Enrique Navarrete_, Aug 31 2018