A136141=A053778(?)

[Maximilian Hasler]

It seems to me that the following are the same:
http://research.att.com/~njas/sequences/?q=id%3AA053778%7Cid%3AA136141

I agree that the older one has a complicated definition:
%N A053778 Lesser of twin primes with property that no non-twin prime
occurs until the next twin.

AFAICS this means: the next prime must be the lesser of a twin,
thus it would be the same as

%N A136141 First of four consecutive primes that are two sets of twin primes.

Apart from (not quite optimized) PARI code, the new one does not seem
to contain any additional information (the link to PrimeQuadruplet, of
course in
A007530, needs not to be duplicated here, IMO).
But I'm in favour of replacing the old %N by the new one.

Maximilian

PS: simpler PARI code would be:
forprime(p=1,10^5, isprime(p+2) & isprime(2+nextprime(p+3)) & print1(p,","))

(in order to avoid flames for "unreadable code", I resist to the
temptation to use the "o+2==(o=p) | next" hack, which would make it a
bit less trivial and 1/3 faster...)