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 A133503 Numbers for which iteration of the powertrain map of A133500 takes a record number of steps to converge. 2
 0, 10, 24, 26, 39, 3573, 26899, 68697, 497699, 3559595 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Where records occur in A133501. This sequence is almost certainly finite. The number 31395559595973 takes 16 steps to converge and may be the next term. It may also be the last term. The next term is > 10^7 (and <= 31395559595973). LINKS EXAMPLE The smallest number that takes 13 steps to converge is 497699, for which the trajectory is 497699 -> 11948427342082473984 -> 23554621393597287150649344 -> 2030652382202824185652602470400000 -> 101921587200000000 -> 38281250 -> 1679616 -> 1452729852 -> 1318305830625 -> 70312500 -> 96 -> 531441 -> 500 -> 0. The smallest number that takes 15 steps to converge is 3559595 -> for which the trajectory is 3559595 -> 4634857177734375 -> 23122964691361341376561152 -> 1194842734208247398400000000 -> 23554621393597287150649344 -> 2030652382202824185652602470400000 -> 101921587200000000 -> 38281250 -> 1679616 -> 1452729852 -> 1318305830625 -> 70312500 -> 96 -> 531441 -> 500 -> 0. The number 31395559595973 takes 16 steps to converge and so the next term is >= 16. The trajectory is 31395559595973 -> 471570692025125026702880859375 -> 34755118508614725279865110528 -> 23122964691361341376561152000000 -> 1194842734208247398400000000 -> 23554621393597287150649344 -> 2030652382202824185652602470400000 -> 101921587200000000 -> 38281250 -> 1679616 -> 1452729852 -> 1318305830625 -> 70312500 -> 96 -> 531441 -> 500 -> 0. CROSSREFS See A133508 for the corresponding numbers of steps. Cf. A133500, A133501. See also A003001. Sequence in context: A223415 A187629 A175403 * A175425 A076675 A063925 Adjacent sequences:  A133500 A133501 A133502 * A133504 A133505 A133506 KEYWORD nonn,base AUTHOR J. H. Conway and N. J. A. Sloane, Dec 03 2007, Dec 04 2007, Dec 18 2007 STATUS approved

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Last modified August 5 10:38 EDT 2021. Contains 346466 sequences. (Running on oeis4.)