A225633 Number of steps to reach a fixed point (A003418(n)), when starting from partition {1+1+1+...+1} of n and continuing with the process described in A225632.

0, 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 5, 5, 5, 6, 6, 7, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 9, 10, 10, 9, 10, 9, 11, 11, 11, 11, 12, 11, 12, 12, 12, 11, 12, 12, 12, 11, 11, 11, 12, 12, 13, 12, 12, 13, 13, 12, 13, 12, 12, 12, 13, 13, 14, 14

Offset: 0

Author

Antti Karttunen, May 13 2013

Keywords

• nonn

Comments

a(0)=0, as its only partition is an empty partition {}, and by convention lcm()=1, thus it takes no steps to reach from 1 to A003418(0)=1.

The records occur at positions 0, 2, 3, 5, 9, 11, 13, 19, 27, 31, 38, 43, 47, 61, 73, 81, ... and they seem to occur in order, i.e., as A001477. Thus the record-positions probably also give the left inverse function for this sequence. It also seems that each integer occurs only finite times in this sequence, so there should be a right inverse function as well.

Crossrefs

Cf. A225634, A225643, A225629, A225654, A226056.

Formula

a(n) = A225634(n) - 1.