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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 (list; graph; refs; listen; history; text; internal format)
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 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.
LINKS
FORMULA
a(n) = A225644(n) - 1.
PROG
(Scheme) (define (A225643 n) (-1+ (A225644 n)))
CROSSREFS
Sequence in context: A212218 A321162 A008668 * A116563 A076695 A071903
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 15 2013
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)