A284987 Juggler sequence starting at 37.

37, 225, 3375, 196069, 86818724, 9317, 899319, 852846071, 24906114455136, 4990602, 2233, 105519, 34276462, 5854, 76, 8, 2, 1

Offset: 0

Author

Matt Westwood, Apr 07 2017

Keywords

• nonn
• full
• fini

Comments

Many sources state that the Juggler sequence on 37 is, for example, "the first tall peak in its graph", and "the high water number of steps are" and so on, without specifically giving the actual sequence. As this specific instance is cited in various places as a specific instance, if not a special case, it seems worthy to document it here explicitly.

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, 1997, page 99.

Links

• Eric Weisstein's World of Mathematics, Juggler Sequence
• Calculated using the Juggler Sequence calculator found at Calculation for it

Crossrefs

Cf. A007320, A094670, A094683.

Programs

PARI

Juggler(n)={my(L=List([n])); while(n<>1, n=sqrtint(n^(2-(-1)^n)); listput(L,n)); Vec(L)}
{ Juggler(37) } \\ Andrew Howroyd, Apr 27 2020

Formula

a(0) = 37, a(n) = floor(sqrt(a(n-1))): n even, a(n) = floor((sqrt(a(n-1)))^3): n odd.