A095911 Number of steps where the modified Juggler sequence reaches a new record (A095910).

1, 6, 13, 19, 21, 62, 64, 83, 94, 112, 120, 142, 144, 301, 306, 311, 322, 338, 357

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.

The records A094696 and A095911 are probably the same sequence. - R. J. Mathar, Jul 28 2007

Crossrefs

Cf. A007321, A095909, A095910.

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]; Print[n]], {n, 250000}]

Extensions

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