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A131461
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Residues of 3^(2^p(n)-2) for Mersenne numbers with prime indices.
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6
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0, 1, 1, 1, 1013, 1, 1, 1, 5884965, 65165529, 1, 103888408793, 474639880182, 4112907695371, 72685811469476, 5155089749987738, 440411515280180314, 1, 95591506202441271281, 69291880649932219827
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OFFSET
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1,5
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COMMENTS
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M_p is prime iff 3^(M_p-1) is congruent to 1 mod M_p. Thus M_7 = 127 is prime because 3^126 mod 127 = 1 while M_11 = 2047 is composite because 3^2046 mod 2047 <> 1.
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LINKS
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FORMULA
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a(n) = 3^(2^p(n)-2) mod 2^p(n)-1
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EXAMPLE
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a(5) = 3^(2^11-2) mod 2^11-1 = 3^2046 mod 2047 = 1013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Dennis Martin (dennis.martin(AT)dptechnology.com), Jul 20 2007
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STATUS
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approved
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