This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133503 #14 Jan 24 2022 20:51:48 %S A133503 0,10,24,26,39,3573,26899,68697,497699,3559595,555959597395 %N A133503 Numbers for which iteration of the powertrain map of A133500 takes a record number of steps to converge. %C A133503 Where records occur in A133501. %C A133503 This sequence is almost certainly finite. %C A133503 The number 31395559595973 takes 16 steps to converge and may be the next term. It may also be the last term. %C A133503 The next term is > 10^7 (and <= 31395559595973). %e A133503 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 A133503 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 A133503 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. %e A133503 The smallest number that takes 16 steps to converge is 555959597395, for which the trajectory starts 555959597395 -> 471570692025125026702880859375 and then continues as above. - _Michael S. Branicky_, Jan 24 2022 %Y A133503 See A133508 for the corresponding numbers of steps. Cf. A133500, A133501. %Y A133503 See also A003001. %K A133503 nonn,base %O A133503 1,2 %A A133503 _J. H. Conway_ and _N. J. A. Sloane_, Dec 03 2007, Dec 04 2007, Dec 18 2007 %E A133503 a(11) from _Michael S. Branicky_, Jan 24 2022