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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. 3

%I

%S 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,

%T 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,

%U 12,12,13,12,12,13,13,12,13,12,12,12,13,13,14,14

%N 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.

%C 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.

%C 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.

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

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

%K nonn

%O 0,4

%A _Antti Karttunen_, May 13 2013

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Last modified March 7 10:38 EST 2021. Contains 341869 sequences. (Running on oeis4.)