New primes sequence : Primes for which SQRT(A000040(n)) < A001223(n)

[reismann at free.fr]

Dear Seqfans,

I will submit this sequence in January :

%I A000001
%S A000001 3,7,13,23,31,113
%N A000001 Primes for which SQRT(A000040(n)) < A001223(n).
%C A000001 Conjecture : this sequence is finite and complete.
%e A000001 a(1) = 3 because SQRT(3) < 2.
a(6) = 113 because SQRT(113) < 14.
%Y A000001 A000040(n), A001223(n).
%O A000001 1,1
%K A000001 ,fini,nonn,
%A A000001 Remi Eismann (reismann at free.fr), Dec 10 2006

Any comments on the sequence or on the conjecture ?
Have a nice day.

Rémi EISMANN