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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).
4
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
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
Sequence in context: A032027 A360863 A005383 * A175257 A190423 A278024
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Mar 12 2019
EXTENSIONS
More terms from Amiram Eldar, Mar 12 2019
STATUS
approved