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

0,1

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

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Juggler Sequence

Calculated using the Juggler Sequence calculator found at Calculation for it

Formula

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

Prog

(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

Crossrefs

Cf. A007320, A094670, A094683.

Sequence in context: A052166 A142010 A230006 * A133958 A088544 A051463

Adjacent sequences: A284984 A284985 A284986 * A284988 A284989 A284990

Keyword

nonn,full,fini

Author

Matt Westwood, Apr 07 2017

Status

approved