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A306826
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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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4
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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