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

0,2

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

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 *)

Crossrefs

Cf. A175257, A307244.

Sequence in context: A032027 A360863 A005383 * A175257 A190423 A278024

Adjacent sequences: A306823 A306824 A306825 * A306827 A306828 A306829

Keyword

nonn

Author

Thomas Ordowski, Mar 12 2019

Extensions

More terms from Amiram Eldar, Mar 12 2019

Status

approved