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Search: id:A131459
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| A131459 |
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Residues of 3^(2^(p(n)-1)) for Mersenne numbers with prime indices. |
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+0
6
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| 0, 4, 28, 124, 601, 8188, 131068, 524284, 5758678, 269332797, 2147483644, 60499757946, 322343434415, 5567835897839, 16557488261208, 7853427629182494, 426047939903614778, 2305843009213693948, 141920345591572240917
(list; graph; listen)
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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)) is congruent to (-3) Mod Mp. Thus M7 = 127 is prime because 3^64 Mod 127 = 124 (=127-3) while M11 = 2047 is composite because 3^1024 Mod 2047 <> 2044.
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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)) Mod 2^p(n)-1
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EXAMPLE
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a(5) = 3^(2^(11-1)) Mod 2^11-1 = 3^1024 Mod 2047 = 601
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CROSSREFS
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Cf. A095847, A001348, A131458, A131460, A131461, A131462, A131463.
Sequence in context: A077595 A092712 A058227 this_sequence A139736 A128941 A051536
Adjacent sequences: A131456 A131457 A131458 this_sequence A131460 A131461 A131462
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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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