

A225643


Number of steps to reach a fixed point (A003418(n)), when starting from partition {n} of n and continuing with the process described in A225642.


4



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

0,6


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, 3, 5, 9, 11, 13, 19, 27, 30, 33, 43, 44, 51, 65, 74, 82, ... and they seem to occur in order, i.e., as A001477. Thus the recordpositions 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.


LINKS

Table of n, a(n) for n=0..75.


FORMULA

a(n) = A225644(n)  1.


PROG

(Scheme) (define (A225643 n) (1+ (A225644 n)))


CROSSREFS

Cf. A225644, A225633, A225639, A226055, A226056.
Sequence in context: A212218 A321162 A008668 * A116563 A076695 A071903
Adjacent sequences: A225640 A225641 A225642 * A225644 A225645 A225646


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 15 2013


STATUS

approved



