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

[reismann at free.fr]

Dear Seqfans

Primes p smaller than sqrt(g)*exp(sqrt(g)), with g gap of p :
2, 3, 5, 7, 13, 23, 113, 1327, 31397, 370261, 2010733, 20831323...
and the associated gaps :
1, 2, 2, 4, 4, 6, 14, 34, 72, 112, 148, 210...
There are no other terms less than 49979687.
In connection with Wolf's conjecture.

Best

Rémi Eismann

Selon 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
>