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Search: id:A131460
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| A131460 |
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Residues of 3^(2^(p(n)-1)+1) for Mersenne numbers with prime indices. |
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+0
6
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| 0, 5, 22, 118, 1803, 8182, 131062, 524278, 498820, 271127480, 2147483638, 44060320367, 967030303245, 7907414671310, 49672464783624, 5545884378065500, 125222315103997360, 2305843009213693942, 130613131595363896897
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OFFSET
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1,2
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COMMENT
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Mp is prime iff 3^(2^(p(n)-1)+1) is congruent to (-9) Mod Mp. Thus M7 = 127 is prime because 3^65 Mod 127 = 118 (=127-9) while M11 = 2047 is composite because 3^1025 Mod 2047 <> 2038.
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LINKS
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Dennis Martin, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = 3^(2^(p(n)-1)+1) Mod 2^p(n)-1
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EXAMPLE
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a(5) = 3^(2^(11-1)+1) Mod 2^11-1 = 3^1025 Mod 2047 = 1803
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CROSSREFS
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Cf. A095847, A001348, A131458, A131459, A131461, A131462, A131463.
Sequence in context: A127620 A122951 A020003 this_sequence A062794 A036235 A020077
Adjacent sequences: A131457 A131458 A131459 this_sequence A131461 A131462 A131463
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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 13 2007, Jul 20 2007
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