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A083391
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n-th Payam number E_{-}(n), defined as the smallest positive odd integer k such that for every positive integer n, the number k*2^n-1 is not divisible by any primes p such that the multiplicative order of 2 mod p is less than or equal to e.
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1
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3, 3, 45, 45, 45, 45, 45, 45, 2145, 2805, 92235, 92235, 92235, 92235, 92235, 92235, 529815, 529815, 529815, 529815, 529815, 529815, 529815, 529815, 1426425, 1426425, 247016055, 247016055, 247016055, 247016055
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OFFSET
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2,1
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COMMENTS
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Payam numbers yield many primes of the form k*2^n+1 (Proth primes) and k*2^n-1.
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LINKS
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EXAMPLE
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E_{-}(4) = 45 because 45 is the smallest odd integer k such that for every nonnegative integer n, k*2^n-1 is not divisible by 3, 5, or 7, the only primes p for which the multiplicative order of 2 mod p is less than or
equal to 4.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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