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

Author

Thomas Ordowski, Mar 12 2019

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

Cf. A175257, A307244.

Programs

Mathematica

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 *)

Extensions

More terms from Amiram Eldar, Mar 12 2019