don't understand A056784

[Richard Mathar]

I have problems in deciphering the connection between the description
and the actual numbers in A056784:

The counts of consecutive nonprimes at 1,8,24,90,1832,30594,81464,
404598 etc
are 1 (1..1),
3 (8..10),
5 (24..28),
7 (90..96),
15 (1832..1846),
37 (30594..30630),
45 (81464..85508),
73 (404598..404670)
115 (5845194..5845308)
and do not match the definition because 5 is less than 2*3, 7 is less than
2*5, 45 is less than 2*37 and 73 less than 2*45 etc.

The sequence I would have expected is 1,8,90,524,9552,31398,2010734,..
associated with run lengths of 1,3,7,17,35,71,147,..
(and loosely related to one plus a number in A002386)
for "First nonprime in a sequence of consecutive nonprimes which is
at least twice as long as any earlier run of consecutive nonprimes of this list"

If the meaning is
"First nonprime in a sequence of consecutive nonprimes which is
at least twice as long as any earlier run of consecutive nonprimes"
then the sequence starts 1,8 and is followed by a huge number that I am not
able to compute (because it would mean that there is a prime gap that is
twice as large as any earlier prime gap which is unlikely to exist).

Richard