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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)