cp's OEIS Frontend

Let points 2, 3, & 1 be placed on a straight line at intervals of 1 unit. At point 1 make a half unit circle then at point 2 make another half circle; by selecting radius point on the left hand side of point 1 (pattern 1); at point 3 make another half circle and maintain continuity of circumferences. Continue using this procedure at point 1, 2, 3, ... and so on.

Conjecture: All forms of 3 center points are non-expanded loops.

There are other sets of center points that give the same sequence, e.g.: [2,3,1,4]; [3,2,4,1]; [3,2,4,1,5]; [2,3,1,4,5,7,6]; [2,3,1,7,4,6,5]; [3,4,2,5,1,6,7]; [4,3,5,6,2,7,1]; [4,5,3,2,1,6,7]; [5,4,6,3,2,7,1].

Also, there are some similar patterns that give difference sequences, e.g.:

A047622: [1,2,7,3,4,6,5]; [1,2,7,6,3,5,4]...

A047399: [1,2,7,3,6,4,5]; [1,2,7,6,5,3,4]...

A047395: [2,3,1,4 7,5,6]; [2,3,1,7,6,4,5]...

A047464: [4,5,3,6,2,7,1]; [1,8,2,7,3,6,4,5];

[9,1,8,2,7,3,6,4,5].

See illustration in links.

Appears to be basically a duplicate of A047618. - R. J. Mathar, Feb 03 2014