A175257 -id:A175257 - cp's OEIS frontend

A306826 a(0) = 1; a(n) is the 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, 172849951, 345699901, 352755001, 564408001, 634959001, 793698751, 793886887, 4763321317, 4822127753

Offset: 0

Thomas Ordowski, Mar 12 2019

nonn

For n > 0, a(n) is prime or pseudoprime (a Fermat pseudoprime to base 2).
It seems that for any odd initial term a(0), this recursion gives at most finitely many composite terms (which were not found in this sequence).
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.

Amiram Eldar, Table of n, a(n) for n = 0..1000

Cf. A175257, A307244.

A = {1}; While[Length[A] < 500, a = Last[A]; r = MultiplicativeOrder[2, a]; k = a + r; While[PowerMod[2, k - 1, k a] != 1, k = k + r];  AppendTo[A, k]]; Take[A, 75] (* Emmanuel Vantieghem, Apr 02 2019 *)

More terms from Amiram Eldar, Mar 12 2019

cp's OEIS Frontend

A306826 a(0) = 1; a(n) is the smallest integer k > a(n-1) such that 2^(k-1) == 1 (mod a(n-1)*k).

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