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n-th run has length n-th prime, with digits 0 and 1 only, starting with 0.
4

%I #5 Nov 28 2018 15:22:24

%S 0,0,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1

%N n-th run has length n-th prime, with digits 0 and 1 only, starting with 0.

%e .n ..... Run ....................... Length

%e .1 ..... 0,0 ....................... 2

%e .2 ..... 1,1,1 ..................... 3

%e .3 ..... 0,0,0,0,0 ................. 5

%e .4 ..... 1,1,1,1,1,1,1 ............. 7

%e .5 ..... 0,0,0,0,0,0,0,0,0,0,0 ..... 11

%t With[{nn=11},Riffle[Table[PadRight[{},Prime[n],0],{n,1,nn,2}],Table[ PadRight[ {},Prime[n+1],1],{n,1,nn,2}]]//Flatten] (* _Harvey P. Dale_, Nov 28 2018 *)

%Y Cf. A000040, A057212.

%K easy,nonn

%O 1,1

%A _Omar E. Pol_, Mar 29 2008