A185184 Steps of the Hare in each tied Hare and Tortoise race of length n.

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, 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, 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

Offset

1,3

Comments

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

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.

Links

Table of n, a(n) for n=1..134.

Jason Kimberley, Bits, flows, and compositions

Formula

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

Example

The table begins:
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 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 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;
Mapping between sequences:
A030302: 110111001011101111000100110101011110011011110111110000100011
A185184:  10211003021102111000400310202021110031021110211110000500041
A066099:  1 211  3 211 2111   4  31 2 2 2111  31 2111 21111    5   41

Crossrefs

Sequence in context: A250622 A212551 A125753 * A292894 A147701 A228348

Adjacent sequences: A185181 A185182 A185183 * A185185 A185186 A185187

Keyword

nonn,easy,tabf

Author

Jason Kimberley, Feb 27 2012

Status

approved