Postgres 16

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with recursive data as (

select

n as len,

(20 - n * (n + 1) / 2) / n + 1 as range,

floor((sqrt(8 * 20 + 1) - 1) / 2)::int as maxlen

from generate_series(2, floor((sqrt(8 * 20 + 1) - 1) / 2)::int) n

), candidates as (

select ofs + 1 s, ofs + len e,

row_number() over (partition by ofs order by len desc) as rnk

from data cross join generate_series(0, (select max(range) - 1 from data)) ofs

/* last second half of the condition eliminates some un-useful series up front */

where ofs < range and (len = maxlen or ofs >= maxlen)

and 20 - (ofs + 1 + (len - 1) / 2::float) * len < ofs + len + 1

), chain as (

select * from candidates where s = 1

union all

select rc.* from chain c inner join candidates rc on rc.s = c.e + 1

)

select s, least(e, 100) as e from chain where s <= 100

union all

select n, n from generate_series((select max(e) + 1 from chain), 100) n

order by s;

SELECT 94