Postgres 14

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select version();

version

PostgreSQL 14.10 on x86_64-pc-linux-gnu, compiled by gcc (GCC) 8.5.0 20210514 (Red Hat 8.5.0-20), 64-bit

SELECT 1

create table nums (
  number bigint not null primary key
);

insert into nums values (123), (1234), (12345), (123456), (111), (1111), (2), (700); 

select * from nums;

create table numchar as
  select number::text from nums;

select * from numchar;

CREATE TABLE

INSERT 0 8

number

123

1234

12345

123456

111

1111

2

700

SELECT 8

SELECT 8

number

123

1234

12345

123456

111

1111

2

700

SELECT 8

select min(a.number) as root, b.number as derivative
  from nums a
       cross join lateral generate_series(1, 18) as gs(power)
       join nums b 
         on b.number / (10^gs.power)::bigint = a.number
 group by b.number
 order by root, derivative;

root
derivative

111
1111

123
1234

123
12345

123
123456

SELECT 4

with groupings as (
  select number, 
         case
           when number like (lag(number) over (order by number))||'%' then 0
           else 1
         end as newgroup
    from numchar
), groupnums as (
  select number, sum(newgroup) over (order by number) as groupnum
    from groupings
), matches as (
  select min(number) over (partition by groupnum) as root,
         number as derivative
    from groupnums
)
select *
  from matches
 where root != derivative;

root
derivative

111
1111

123
1234

123
12345

123
123456

SELECT 4