A185184 - OEIS

%I #16 Apr 08 2020 00:08:14

%S 1,0,2,1,1,0,0,3,0,2,1,1,0,2,1,1,1,0,0,0,4,0,0,3,1,0,2,0,2,0,2,1,1,1,

%T 0,0,3,1,0,2,1,1,1,0,2,1,1,1,1,0,0,0,0,5,0,0,0,4,1,0,0,3,0,2,0,0,3,1,

%U 1,0,2,0,0,3,0,2,0,2,1,0,2,1,0,2,0,2,1,1,1,1,0,0,0,4,1,0,0,3,1,1,0,2,0,2,1,0,2,1,1,1,1,0,0,3,1,1,0,2,1,1,1,1,0,2,1,1,1,1,1,0,0,0,0,0

%N Steps of the Hare in each tied Hare and Tortoise race of length n.

%C When the Hare bothers to move it only ever just catches up to the Tortoise.

%C This is an intermediate sequence between A030302 and A066099: omit the 0's from this sequence and we obtain A066099; map nonzero terms in this sequence to 1 and we obtain A030302.

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/A185184">Bits, flows, and compositions</a>

%F a(i) = A030302(i) + number of consecutive 0 terms immediately preceding A030302(i).

%e The table begins:

%e 1;

%e 0 2, 1 1;

%e 0 0 3, 0 2 1, 1 0 2, 1 1 1;

%e 0 0 0 4, 0 0 3 1, 0 2 0 2, 0 2 1 1, 1 0 0 3, 1 0 2 1, 1 1 0 2, 1 1 1 1;

%e 0 0 0 0 5, 0 0 0 4 1, 0 0 3 0 2, 0 0 3 1 1, 0 2 0 0 3, 0 2 0 2 1, 0 2 1 0 2, 0 2 1 1 1, 1 0 0 0 4, 1 0 0 3 1, 1 0 2 0 2, 1 0 2 1 1, 1 1 0 0 3, 1 1 0 2 1, 1 1 1 0 2, 1 1 1 1 1;

%e Mapping between sequences:

%e A030302: 110111001011101111000100110101011110011011110111110000100011

%e A185184:  10211003021102111000400310202021110031021110211110000500041

%e A066099:  1 211  3 211 2111   4  31 2 2 2111  31 2111 21111    5   41

%K nonn,easy,tabf

%O 1,3

%A _Jason Kimberley_, Feb 27 2012