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a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(n-2), a(n-3), and a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=3.
1

%I #9 Apr 19 2018 17:37:10

%S 0,1,2,3,4,5,6,7,8,9,10,22,33,44,55,11,20,36,47,58,19,200,63,74,85,91,

%T 202,66,34,57,18,29,60,43,75,81,92,600,333,45,17,28,69,30,54,71,82,96,

%U 300,444,15,27,68,39,40,51,72,86,93,400,111,25,67,38,49,100

%N a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(n-2), a(n-3), and a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=3.

%C The first differences of this sequence are symmetrically distributed in a distribution that has a larger kurtosis than the Normal distribution.

%C It seems that appart from the initial terms, 39 and 40 are the only consecutive terms.

%C Unlike A298482, 3-digit terms appear as early as a(22)=200.

%H Rémy Sigrist, <a href="/A301801/a301801.gp.txt">PARI program for A301801</a>

%t Nest[Append[#, Block[{k = 4, d}, While[Nand[FreeQ[#, k], ! IntersectingQ[Union@ Apply[Join, Take[#[[All, -1]], -4] ], Set[d, IntegerDigits[k]]] ], k++]; {k, d}]] &, Transpose@ {#, IntegerDigits@ #} &@ Range[0, 3], 62][[All, 1]] (* _Michael De Vlieger_, Apr 12 2018 *)

%o (PARI) See Links section.

%Y Cf. A067581, A276633, A298482.

%K nonn,base

%O 0,3

%A _Enrique Navarrete_, Mar 26 2018