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Record numbers of steps associated with the terms of A133503.
2

%I #11 Jan 24 2022 20:52:12

%S 0,1,2,5,9,10,11,12,13,15,16

%N Record numbers of steps associated with the terms of A133503.

%C This sequence is almost certainly finite.

%e 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.

%e 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.

%e The number 31395559595973 takes 16 steps to converge and so the next term is >= 16.

%e The trajectory of 31395559595973 is 31395559595973 -> 471570692025125026702880859375 -> 34755118508614725279865110528 -> 23122964691361341376561152000000 -> 1194842734208247398400000000 -> 23554621393597287150649344 -> 2030652382202824185652602470400000 -> 101921587200000000 -> 38281250 -> 1679616 -> 1452729852 -> 1318305830625 -> 70312500 -> 96 -> 531441 -> 500 -> 0.

%Y Cf. A133500, A133501, A133503.

%K nonn,base,more

%O 1,3

%A _J. H. Conway_ and _N. J. A. Sloane_, Dec 04 2007, Dec 18 2007

%E a(11) from _Michael S. Branicky_, Jan 24 2022