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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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. LINKS FORMULA a(n) = A225634(n) - 1. CROSSREFS Cf. A225634, A225643, A225629, A225654, A226056. Sequence in context: A285507 A103264 A225644 * A060960 A073642 A262869 Adjacent sequences:  A225630 A225631 A225632 * A225634 A225635 A225636 KEYWORD nonn AUTHOR Antti Karttunen, May 13 2013 STATUS approved

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Last modified January 21 15:16 EST 2021. Contains 340352 sequences. (Running on oeis4.)