[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]

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)?

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]

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

[Guest]

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

I agree with DeeGee.

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