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A133503
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Numbers for which iteration of the powertrain map of A133500 takes a record number of steps to converge.
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2
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..10.
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EXAMPLE
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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.
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CROSSREFS
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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
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KEYWORD
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nonn,base
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AUTHOR
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J. H. Conway and N. J. A. Sloane, Dec 03 2007, Dec 04 2007, Dec 18 2007
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STATUS
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approved
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