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A083556
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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, 9, 15, 105, 105, 105, 105, 105, 165, 165, 75075, 75075, 75075, 75075, 75075, 75075, 855855, 855855, 5583435, 5583435, 5583435, 18625035, 18625035, 18625035, 18625035, 18625035, 27183585, 27183585, 27183585, 27183585, 27183585
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Payam numbers are good candidates for looking for Proth primes, i.e. primes of the form k*2^n+1
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LINKS
| Author?, Title?
Eric Weisstein's World of Mathematics, Payam Number
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EXAMPLE
| E_{+}(3) = 9 because 9 is the smallest odd integer k such that for every nonnegative integer n, k*2^n+1 is not divisible by 3 or 7, the only primes p for which the multiplicative order of 2 mod p is less than or equal to 3.
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CROSSREFS
| Cf. A080076.
Cf. A083391.
Sequence in context: A192165 A050869 A038547 * A015664 A134137 A174179
Adjacent sequences: A083553 A083554 A083555 * A083557 A083558 A083559
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KEYWORD
| hard,nonn
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AUTHOR
| David Terr (davidcterr(AT)aol.com), Jun 10 2003
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