create table running_log ( 
  run_date          date not null,  
  time_in_seconds   int  not null, 
  distance_in_miles int  not null 
)

begin 
  insert into running_log values (date'2018-01-01', 420, 1); 
  insert into running_log values (date'2018-01-02', 2400, 5); 
  insert into running_log values (date'2018-01-03', 2430, 5); 
  insert into running_log values (date'2018-01-06', 2350, 5); 
  insert into running_log values (date'2018-01-07', 410, 1); 
  insert into running_log values (date'2018-01-10', 400, 1); 
  insert into running_log values (date'2018-01-13', 2300, 5); 
  insert into running_log values (date'2018-01-14', 425, 1); 
  insert into running_log values (date'2018-01-15', 422, 1); 
  commit; 
end; 

select * from running_log

Model Clause Solution

select * from running_log   
model    
  dimension by ( row_number() over (order by run_date) rn )    
  measures ( run_date, 1 grp, run_date grp_start )   
  rules (   
    grp_start[1] = run_date[cv()],   
    grp_start[any] =    
      case    
        when run_date[cv()] < grp_start[cv()-1] + 7 then grp_start[cv() - 1]     
        else run_date[cv()]    
      end ,   
    grp[any] =    
      case    
        when run_date[cv()] < grp_start[cv()-1] + 7 then grp[cv() - 1]   
        else nvl(grp[cv() - 1] + 1, 1)   
      end    
  )

Recursive Subquery Factoring solution

with rws as (  
  select r.*,   
         row_number() over (order by run_date) rn  
  from   running_log r  
), within_7 (  
  run_date, time_in_seconds, distance_in_miles, rn, grp, grp_start  
) as (  
  select run_date, time_in_seconds, distance_in_miles, rn,  
         1 grp, run_date grp_start  
  from   rws  
  where  rn = 1  
  union all  
  select r.run_date, r.time_in_seconds, r.distance_in_miles, r.rn,  
         case   
           when r.run_date < w.grp_start + 7 then grp   
           else grp + 1  
         end grp,   
         case   
           when r.run_date < w.grp_start + 7 then grp_start  
           else r.run_date  
         end grp_start  
  from   within_7 w  
  join   rws r  
  on     w.rn + 1 = r.rn  
)  
  select w.run_date,   
         dense_rank() over (order by grp_start) grp,  
         grp_start  
  from   within_7 w

Pattern Matching Solution

select *   
from   running_log   
match_recognize (  
  order by run_date  
  measures   
    match_number() as grp,  
    first(run_date) as grp_start  
  all rows per match  
  pattern ( strt within_7* )  
  define   
    within_7 as run_date < ( first ( run_date ) + 7 )  
)