A303294 - OEIS

A303294

a(n) is the least positive integer not yet in the sequence which shares a digit with either a(n-3) or a(n-2) (or with both), but shares no digit with a(n-1); a(1)=0, a(2)=1, a(3)=2.

%I #20 May 08 2018 15:58:37

%S 0,1,2,10,22,11,20,13,24,3,4,12,30,14,23,15,26,5,6,21,35,16,25,17,28,

%T 7,8,27,18,29,31,9,32,19,33,41,36,40,37,42,38,44,39,45,63,47,50,34,51,

%U 43,52,46,53,48,55,49,56,74,58,60,54,61,57,62,59

%N a(n) is the least positive integer not yet in the sequence which shares a digit with either a(n-3) or a(n-2) (or with both), but shares no digit with a(n-1); a(1)=0, a(2)=1, a(3)=2.

%C Apparently there exist only 5 pairs of consecutive integers belonging this sequence, a(k+1)-a(k)=1 for k in (1,2,10,18,26). Respectively those pairs are: (0;1), (1;2), (3;4), (5;6), and (7;8).

%C It seems that a(j)=j only for j in (12,14,31,53,55,60,71,73,75,82,84,95,102). - _R. J. Cano_, Apr 22 2018

%H R. J. Cano, <a href="/A303294/b303294.txt">Table of n, a(n) for n = 1..10000</a>

%H R. J. Cano, <a href="/A303294/a303294_2.txt">A sequencer program in PARI.</a>

%e a(10)=3 since it shares a digit (3) with a(8)=13, and shares no digit with a(9)=24.

%o (PARI) See Cano link.

%Y Cf. A286890, A300907, A302566, A302388.

%K nonn,base

%O 1,3

%A _Enrique Navarrete_, Apr 20 2018