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Search: id:A123159
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| A123159 |
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Conjectured smallest Sierpinski numbers of the second kind S, base b=2,3,4,5..., where P*S*b^n+1 is composite for all n and S = the multiple of all primes which have multiplicative order base b of 1. |
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+0
1
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OFFSET
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2,1
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COMMENT
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Some values of with base b=2^x+1 for integers x have also been calculated - see the links.
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REFERENCES
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G. Jaeschke, "On the smallest k such that k * 2n +1 are composite," Math. Comp., 40:181 (1983) 381-384. MR 84k:10006
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LINKS
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base=2^x+1
base=3
base=5
base=4
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EXAMPLE
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For base=3, the multiplicative order of 2 base 3 is 1 and therefore the formula is 2*S*3^n+1. Find a covering set of multiplicative orders of primes base b and discover S by trial and error using the Chinese Remainder Theorem.
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CROSSREFS
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Sequence in context: A038826 A038815 A076336 this_sequence A157661 A159713 A103873
Adjacent sequences: A123156 A123157 A123158 this_sequence A123160 A123161 A123162
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KEYWORD
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hard,more,nonn
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AUTHOR
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Robert Smith (robert_smith44(AT)hotmail.com), Oct 02 2006
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