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Where the modified Juggler sequence reaches a new record.
4

%I #14 Mar 09 2023 02:09:21

%S 2,3,7,25,73,101,471,549,791,837,1199,2267,29773,38653,273317,2776203,

%T 3683335,4975111,8087437

%N Where the modified Juggler sequence reaches a new record.

%C The modified Juggler sequence: begin with x and if x is even, round(sqrt(x)) -> x and if x is odd, round(sqrt(x3)) -> x and repeat until x = 1, count the iterations.

%C 273317 reaches a maximum of 1640703316...(skip the next 35800 digits)...2531417380 during its trip to 1.

%C Comment from _R. J. Mathar_, Jul 28 2007: The records A094697 and A095910 are probably the same sequence.

%t mjs[n_] := If[ EvenQ[n], Round[ Sqrt[n]], Round[ Sqrt[n^3]]]; f[n_] := Length[ NestWhileList[mjs, n, # != 1 &]] - 1; a = {0}; Do[ b = f[n]; If[b > a[[ -1]], AppendTo[a, b]], {n, 250000}]; a

%Y Cf. A007321, A095909, A095911.

%K nonn,more

%O 1,1

%A _Robert G. Wilson v_, Jun 14 2004

%E a(16)-a(19) from _Chai Wah Wu_, Aug 18 2016