## A216666 and A216668 sequences

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• Hi, I recently added 2 new sequences to OEIS. A216666 : Smallest integer b such that (b+1)^p - b^p is prime for all primes p
Message 1 of 1 , Oct 4, 2012
Hi,

I recently added 2 new sequences to OEIS.

A216666 : Smallest integer b such that (b+1)^p - b^p is prime for all primes p <= prime(n).
The 8 first terms are 1, 1, 1, 1, 6524, 809652228, 30717523794, 55779743835 and for p=23, a solution is > 336831150306.

A216668 : Smallest integer b > 1 such that for all primes p <= prime(n), (b+1)^p - b^p is prime if and only if 2^p-1 is prime.
The 11 first terms are 2, 2, 2, 296, 296, 369719, 457578, 43410300320, 43410300320, 43410300320, 288975248496 (288975248496 is not yet published at OEIS since it requires approval).
For p=61, a solution is > 2147176502688.

I wonder if lows can roughly express the growth of these sequences.
Maybe something like A(n+1) ~ A(n)^constant

J-L
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