[seqfan] Sequence without composite terms

[Tomasz Ordowski]

Dear SeqFans!

Consider a sequence defined by the recursion:

a(0) = 1; a(n) = smallest integer k > a(n-1) such that 2^(k-1) == 1 (mod
a(n-1)k).

1, 3, 5, 13, 37, 73, 109, 181, 541, 1621, 4861, 9721, 10531, 17551,
29251, 87751, 526501, 3159001, 5528251,
11056501, 44226001, 49385701, 98771401, ...

For n > 0, a(n) is prime or pseudoprime. Conjecture: a(n) is prime for
every n > 0, namely:
a(n) is the smallest odd prime p > a(n-1) such that 2^(p-1) == 1 (mod
a(n-1)), with a(0) = 1.

I am asking for counterexamples (composite terms).

Best regards,

Thomas Ordowski
_______________________
Cf. https://oeis.org/A175257