[superprismatic]

A sequence of numbers is generated by

starting with an initial value n₀ and

computing subsequent values using the

rule n_i+1=n_i+[sqrt(n_i)]. Here

[sqrt(n_i)] represents the greatest

integer in sqrt(n_i). If n₀ has no

predecessor we shall call it a seed.

For example, 11 is a seed since it

cannot be produced by any number

using the rule above.

What is the seed corresponding to

1,000,000 (i.e., the unique value

which generates the sequence

containing 1,000,000 and which has

no predecessor)?

[bushindo]

  On 9/4/2009 at 12:17 AM, superprismatic said:

A sequence of numbers is generated by

starting with an initial value n₀ and

computing subsequent values using the

rule n_i+1=n_i+[sqrt(n_i)]. Here

[sqrt(n_i)] represents the greatest

integer in sqrt(n_i). If n₀ has no

predecessor we shall call it a seed.

For example, 11 is a seed since it

cannot be produced by any number

using the rule above.

What is the seed corresponding to

1,000,000 (i.e., the unique value

which generates the sequence

containing 1,000,000 and which has

no predecessor)?

  Reveal hidden contents

JIZD

Edited September 4, 2009 by bushindo

[Guest]

I'm sorry, I can't resist & I respect the board rules about vulgarity & sexual references & so forth, but if this guy wants to sqrt his seed, that's his business.

Meanwhile, it's a bit late & I'm going to sleep.

[Guest]

  Reveal hidden contents

By brute force and some logic, I got 4031 as the seed for 1,000,000

[Guest]

  On 9/4/2009 at 8:17 AM, DeeGee said:

  Reveal hidden contents

By brute force and some logic, I got 4031 as the seed for 1,000,000

I agree with DeeGee.

  Reveal hidden contents

With 4031 as the seed, n₁₈₇₇ gives 1,000,000.