Part three: Propose your favorite

Kip Murray wrote:
> Part two: If you used J to help you figure out the sequence, tell
> 
> Kip Murray wrote:
>> Verb i. produces takes from the sequence of non-negative integers:
>>
>>     i.20
>> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
>>     i.5
>> 0 1 2 3 4
>>     5 {. i.20
>> 0 1 2 3 4
>>
>> Verb s generates takes from a mystery sequence (no peeking in Sloane, please)
>>
>>     s 13
>> 2 3 7 19 53 131 311 719 1619 3671 8161 17863 38873
>>     s 5
>> 2 3 7 19 53
>>     5 {. s 13
>> 2 3 7 19 53
>>
>> Your mission, should you decide to accept it, is to provide a definition for 
>> s . 
>>   As always, these instructions will
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