A095910 Where the modified Juggler sequence reaches a new record.

2, 3, 7, 25, 73, 101, 471, 549, 791, 837, 1199, 2267, 29773, 38653, 273317, 2776203, 3683335, 4975111, 8087437

Offset: 1

Author

Robert G. Wilson v, Jun 14 2004

Keywords

• nonn
• more

Comments

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.

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

Comment from R. J. Mathar, Jul 28 2007: The records A094697 and A095910 are probably the same sequence.

Crossrefs

Cf. A007321, A095909, A095911.

Programs

Mathematica

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

Extensions

a(16)-a(19) from Chai Wah Wu, Aug 18 2016